Cronkite exhibiteed some skepticism, but never vigorously pursued perhaps the most important story during his tenure:

http://www.realhistoryarchives.com/collections/assassinations/jfk/policoff-stone-JKF.htm

JFK: How the Media Assassinated the Real Story

By Robert Hennelly & Jerry Policoff

...77 percent...reject the Warren Report's conclusions. How did such a tremendous credibility gap come about? ...how did a free press so totally blow one of the biggest stories of the century? ...Village Voice has reviewed hundreds of documents bearing on the media's coverage of the assassination... In particular..CBS, and NBC have striven mightily to protect the single assassin hypothesis, even when that has involved the suppression of information, the coercion of testimony, and the misrepresentation of key evidence.....

CBS

CBS decided to go ahead with a documentary series in the fall of 1966, as the cynicism about the assassination continued to mount...

The CBS effort was nothing if not monumental. ...The 11 CBS marksmen fired 37 firing runs of three shots each; of those, an amazing 17 of the 37 runs were disqualified as Cronkite said "because of trouble with the rifle." And, even with their faster guns and time to practice, the 11 marksmen averaged 5.6 seconds to get off their three shots, with an average of 1.2 hits. Oswald, a notoriously bad shot firing with a slower gun, is alleged to have done much better--... CBS neglected to inform its viewers of the poor total average hit ratio. How did CBS interpret these rifle tests? "It seems reasonable to say that an expert could fire that rifle in five seconds," intoned Walter Cronkite. "It seems equally reasonable to say that Oswald, under normal circumstances, would take longer. But these were not normal circumstances. Oswald was shooting at a president. So our answer is: probably fast enough."

Such lapses may well be explained by a perusal of internal CBS documents,....The documents show the highly unusual role played by one Ellen McCloy, who for years had served as the administrative assistant to Richard Salant, head of CBS News. ...she was more than a passive recipient, filing duplicates for her boss. She was passing along not her own opinions but those of "Dad."

Ellen McCloy's father, John J. McCloy, had not only served on the Warren Commission but had been Assistant Secretary of War, High Commissioner for West Germany, chair of the World Bank, chair of Chase Manhattan Bank, and head of the Ford Foundation. McCloy himself acknowledged his agenda: showing that America was not "a banana republic, where a government can be changed by conspiracy."...

....But the McCloy memos, and a few others, certainly raise a question about how open-minded and thoroughgoing CBS was. ...In CBS's June 28, 1967, program, Cronkite does indeed refer to Oswald's FBI connection in the following fashion: "The question of whether Oswald had any relationship with the FBI or the CIA is not frivolous. The agencies, of course, are silent. Although the Warren Commission had full power to conduct its own independent investigation, it permitted the FBI and the CIA to investigate themselves--and so cast a permanent shadow on the answers."... Danny Schechter's "Beyond JFK: The Question of Conspiracy," features Walter Cronkite conceding that CBS News in 1970 censored Lyndon Johnson's own doubts about the lone-assassin theory. Cronkite tells Schechter that Johnson invoked "national security" to get CBS to edit out his remarks long after they had been captured on film. Cronkite and CBS, of course, reflexively complied. ...

..(Nix) also told CBS that there were four shots fired during the assassination, an observation subsequently endorsed by the House Select Committee on Assassinations in 1975, based on controversial acoustical evidence. But what did the CBS viewing audience hear from Nix? "Bang, bang, bang," as if to suggest that Nix also subscribed to the three-bang theory.

After being browbeaten by CBS, Orville Nix, a normally mild-mannered man, became furious. "He was hitting the steering wheel on the ride back home saying, `Why are they trying to make me feel like I am insane?'"....

How many other witnesses experienced the Orville Nix you-never-heard/saw-that phenomenon we will never know. But one other was Kenny O'Donnell, a confidant and adviser to JFK who was in the motorcade. ..Tip O'Neill's book Man of The House, ..describes a conversation with O'Donnell, who told him he was sure that two shots had come from the fence behind the grassy knoll. O'Neill said to O'Donnell, "That's not what you told the Warren Commission." O'Donnell responded, "You're right, I told the FBI what I had heard, but they said it couldn't have happened that way and that I must have been imagining things. So I testified the way they wanted me to...."

FACT COLLIDES WITH FICTION

...Motive in this crime of omission was no doubt a confluence of many elements: a blind patriotism, an institutional paternalism, and a determination to admit no mistakes. Once wedded to the Warren Commission, the editors and reporters who covered the assassination considered even a whisper of conspiracy a form of infidelity. All others, from Mark Lane to Oliver Stone and the hundreds of enterprising reporters in between, were traitors, hysterics.

Throughout the early 1960s, when Walter Cronkite said, "That's the way it is . . .," we had no reason to doubt him. The bashing of Oliver Stone's movie JFK by the bastions of the American media--CBS, The New York Times, Time, Newsweek, and The Washington Post--is said to spring from the sincere desire on the part of the keepers of America's memory to see that our sacred history does not fall prey to revisionist charlatans. .... "When it came to this [reporting on the assassination], the working press was a lobster in a trap," Bill Moyers told the Voice. "Back then, what government said was the news. . . . In the 1950s and early '60s, the official view of reality was the agenda for the Washington press corps. . . . I think it is quite revealing that it's Oliver Stone that's forcing Congress to open up the files and not The Washington Post, The New York Times, or CBS."