Bill O’Reilly has been embroiled in controversy over some of his past recollections, but if you think he should get the boot, you’re in the minority. Only 12 percent of American voters think the Fox News host should be fired as a result of recent challenges to his accuracy, according to a Quinnipiac University poll released Monday. Another 11 percent say O’Reilly should be suspended, and 23 percent say he should be allowed to continue. More than half of respondents said they haven’t heard enough about the scandal to make a determination.

The poll, based on a telephone survey of 1,286 self-identified registered voters, was conducted Feb. 26-March 2, more than a week after Mother Jones magazine published a story in which journalist David Corn questioned O’Reilly’s account of his coverage of the 1982 Falklands War. Following the Mother Jones article, other outlets published subsequent challenges to different stories O’Reilly has told on the air or in his books. O’Reilly has defended himself on his show, "The O'Reilly Factor," and both Fox News Channel and his publisher, Crown Publishing Group, have stood by the host.

Opinions on what should happen to O’Reilly are sharply divided along party lines. Just 4 percent of Republicans surveyed think O’Reilly should be fired, compared with 21 percent of Democrats. Among independents, 12 percent say he should be fired.

In contrast, a much higher percentage of respondents -- 35 percent -- believe Brian Williams should not be allowed to return to anchor “NBC Nightly News.” Williams was suspended for six months Feb. 10 amid questions surrounding some of his own recollections, most notably a false retelling of having been in a helicopter hit by rocket fire over Iraq. Among Republicans polled by Quinnipiac, 42 percent say Williams should not be allowed to return following his suspension, compared with 28 percent of Democrats.   

The Quinnipiac poll found that Fox News is the most trusted of all the major TV news outlets, with 29 percent of respondents saying they trust the network’s coverage most, compared with 22 percent for CNN, 10 percent for NBC News and CBS News and 8 percent for ABC News. Only 7 percent said MSNBC offers the most trusted coverage.

Overall, however, trust in American media appears to be on the wane. Asked if national TV news is more or less trustworthy than it was in the days of Walter Cronkite, only 7 percent said it was more trustworthy. Almost half -- 48 percent -- said it was less trustworthy, and 35 percent said it was about the same.

“Bring back Uncle Walter, as Brian Williams and Bill O’Reilly get lukewarm support for their journalistic indiscretions,” said Tim Malloy, assistant director of the Quinnipiac University Poll, in a statement. “American news watchers long for an era where the person in the big chair could be truly trusted. And that’s the way it is.”

Read the full results of the poll here.

Christopher Zara is a senior writer who covers media and culture. News tips? Email him here. Follow him on Twitter @christopherzara.