Among the many exemplars of how these long-time “friends and neighbors” believed their powerful government positions enabled them to do anything they wished to do — from the mundane to the most unthinkable acts — the following items succinctly illustrate the point.
Item #1: An Illustration that needs little further elaboration:
Given that both of them commissioned their own foot-high bronze bust-statuettes at about the same time, it would appear to have been an idea they hatched together as permanent proofs of their grandness and brilliance. The key difference however is the number of them that had been produced: In Hoover’s case, the only known bust of himself was on display in the foyer of his house, placed there for his own pleasure.
In Johnson’s case, as the photo above attests, he presented one copy to Pope Paul VI, just before Christmas in 1967.
But he had unknown hundreds (maybe thousands) made, as demonstrated by the fact that he took 200 with him to give away on a trip to the South Pacific two months earlier, according to Merle Miller, who was his personal friend and supporter as well as one of his earliest authorized biographers. 
According to another one of his earliest biographers, who knew him more intimately than any of the others, Doris Kearns-Goodwin, this was merely one of many mementos to his eminence. She wrote that LBJ had produced, in a record-setting White House budget for the purpose, numerous kinds of government-issue souvenirs, all arranged into a “hierarchy of gifts.” Other items included silver bowls, lighters, watches, tie clasps, all inscribed with his “LBJ” trademark; in the case of the silk scarves, they had a special border design with 526 “LBJs” chained together.
According to Bill Gulley, a White House aide who coordinated an operation that, in Johnson’s last days in office in January, 1969, moved tons of government-purchased property — including furnishings and equipment, “LBJ tie pins, wristwatches, rings, cuff links, ladies’ bracelets, lipstick dispensers, gold cigarette lighters costing $1,000 each . . . It was not cheap stuff. They all had presidential seals.” It took ten flights to move all of it from Washington to Texas; the smaller items were apparently put in storage for eventual sale in the souvenir shop at the LBJ Library. 
Ms. Kearnes-Goodwin added that in addition to all of the above items, there were the photos of himself he enthusiastically handed out to the public on his many trips:
“And of course, the countless pictures of the man himself. In the distribution of these photos, Johnson’s enthusiasm seemed strangely disproportionate; he treated the pictures of himself with unabashed pride, the way a grandfather treats pictures of his grandchildren.” 
Item #2: A story which the columnist Jack Anderson had held back seven years, fearing the public’s reaction to Hoover’s despicable lies intended to destroy Dr. King’s reputation even AFTER he had been assassinated
The newspaper clipping, below, is presented to show the first part of Jack Anderson’s screed on what he called Hoover’s “Hoax” to further discredit Martin Luther King Jr., even after he had been assassinated (through a scheme that Hoover himself had personally designed and executed, with LBJ’s support — as detailed within my book Who Really Killed Martin Luther King Jr.? — The Case against Lyndon B. Johnson and J. Edgar Hoover):
Because it is not a very high-quality photocopy, thus difficult to read, I have retyped it verbatim into the document below: 
“Hoover Floated Hoax Story on King”
By Jack Anderson and Les Whitten
The reason Jack Anderson sat on this article for seven years was because, in 1968, Hoover was still seen as a heroic figure by most Americans (the exceptions being practically all African-Americans and the minority of whites who were aware of his hidden, darker side). But by 1975 — when Anderson finally decided to reveal Hoover’s hideous “coup de grâce” — the reality of his heinous reign had finally begun trickling out, mostly through the revelations exposed by the Senate’s Church Committee (formally the United States Senate Select Committee to Study Governmental Operations with Respect to Intelligence Activities). The public outrage over the Watergate scandal finally caused news media to report other abuses by the Central Intelligence Agency (CIA), National Security Agency (NSA) and Federal Bureau of Investigation (FBI). Some of those exposés have been described in other essays within these blog pages (see HERE and HERE).
Item #3: The Unravelling of COINTELPRO Secrets Began Four Years Before the Church Committee’s Revelations, when a Group of Citizen—Activists Burgled an FBI Field Office in Media, Pennsylvania
The break-in of the FBI offices at Media, Pennsylvania in 1971 by an activist group called “The Citizen’s Committee to Investigate the FBI,” led by the late Bill Davidon, who was considered “mastermind and de facto leader” of the committee; the committee later published an 82 page report of their findings as summarized in the endnote.
This act was the catalyst that eventually led to the discovery of more revelations of official misconduct and finally prodded congress into waking up to the outrageously reckless activities of this and other government agencies.
In 1971, both Hoover and Johnson were still alive. Hoover would die, suddenly, the following year and Johnson would follow him in January, 1973. Both must have been mightily worried about their own secrets being exposed in due course.
It took another four years for the piecemeal outrages to generate enough public interest for congress to finally begin its investigation.
The Washington Post, on March 24, 1975 — when it still possessed some journalistic integrity — published the following editorial about the complete lack of congressional oversight of the FBI:
The Senate’s Church Committee in 1975 uncovered some of most dastardly FBI, CIA and NSA secrets, as summarized in my essay subtitled “A Case Study Examination of How LBJ’s Exhortations To Punish War Protestors Produced Torture Methods Akin to Gestapo Tactics“. The charge made by the Church Committee boiled down to this succinct but strongly-worded assertion: 
“The abusive techniques used by the FBI in COINTELPRO from 1956 to 1971 included violations of both state and federal laws prohibiting mail fraud, wire fraud, incitement to violence, sending obscene mail, and extortion. More fundamentally, the harassment of innocent citizens engaged in lawful forms of political expression did serious injury to the First Amendment guarantee of freedom of speech and the right of the people to assemble peaceably and to petition the government for a redress of grievances.”
Finally, the long-delayed congressional scrutiny of the FBI, CIA and assorted other intelligence agencies ended the decades of uncritical treatment by the press and absence of “due diligence” oversight by congress. Out of those revelations, in 1976 congress created the House Select Committee on Assassinations (HSCA), initially a valiant effort to “reinvestigate” the JFK and MLK assassinations (they erroneously thought that RFK’s was solved).
Unfortunately, those efforts were sabotaged by the combined efforts of the alphabet agencies led by the CIA and very little new revelatory evidence of significance, for either of the two assassinations supposedly being “reinvestigated,” was borne when the HSCA was shut down two years later.
Though the worst of the FBI abuses began under President Lyndon Johnson’s reign, since they were exposed during the Nixon administration many people automatically connected them to him, giving LBJ another pass, in this case one of many, in a postmortem context.
Worse still, the meager and partial reforms of the 1970s became more elastic again with time, and by the 1990s new abuses resurfaced. The current (2018-2020) investigations may produce more lasting reforms of these maverick agencies — or not.
 See first paragraph after the bullet list of FBI abuses in the article above, “Hoover Floated Hoax Story on King.”
 Miller, Merle, Lyndon: An Oral Biography, pp. 455-456
 Kearns, Doris, Lyndon Johnson and the American Dream, pp. ix-x
 Kessler, Ronald, Inside the White House, p. 21
 Op. Cit. (Kearns)
 Anderson, Jack, and Les Whitten, The Washington Post, Dec. 17, 1975, p. C 18.
 “Characters of 1971”, Independent Lens, August 15, 2015: http://www.pbs.org/independentlens/content/1971_characters-html/
The Committee’s report (see it here) concluded that the agents were required to make so many reports and other paperwork that it was amazing they had time to “take a sh*t:”
[I]f we are to believe the Media Papers the incredible number of niggling bureaucratic procedures demanded of each FBI agent is overwhelming! All these years we thought our G-Men were out there tracking down kidnappers; pursuing, hotly, bank robbers; staking out the hideouts of Russian spies and making dogged investigations into the homosexual habits of State Department aides, they were really sitting in an office, filling out forms in quadruplicate and bitching about the latest directives from “Bureau,” as FBI headquarters is always described. One such order, which must have caused groans of dismay, was issued on January, 1971, requiring each agent to be weighed once a month in the office with an overweight agent forced to lose his excess poundage and to “be weighed weekly by his supervisor until his weight is brought within Bureau standards.”
Page 20, from which this paragraph comes, follows (the “blocked” comments are the sarcastic notes inserted by the editors of the committee’s report):
 Report of the U.S. Senate, “Select Committee To Study Government Operations With Respect To Intelligence Activities,” (colloquially known as the “Church Committee,” p. 139.