Mr Thompson took the unusual step of e-mailing BBC journalists to deny the New Statesman's cover story, written by John Kampfner, which claimed that Mr Grade had wanted Mr Humphrys to be sacked after an after-dinner speech he made was leaked to the press.
The magazine claimed that the BBC chairman wanted to make an example of Mr Humphrys because of his disdain for "difficult journalists".
But Mr Kampfner stood by his article, which alleged that when the comments were published in The Times, the BBC chairman telephoned several executives demanding that the Radio 4 Today presenter be sacked.
His article also identified a wider malaise in BBC journalism, accusing Mr Grade and Mr Thompson of presiding over a regime that is deferential to authority figures and discourages risk taking.
In an e-mail to BBC News staff, Mr Thompson said: "The New Statesman article claims that the chairman called 'several executives' the weekend the story about John Humphrys' speech first appeared in the paper. Untrue. The only executive the chairman spoke to was me. He did not order me to 'sack' or in any other way admonish John Humphrys.
"The New Statesman says that 'further calls ensued between 14 senior executives, none of whom knew what to do'. Untrue."
Mr Grade ordered an internal investigation into Mr Humphrys' remarks, which were leaked to The Times by Alastair Campbell's former deputy Tim Allan. In an after-dinner speech, the Today presenter accused some politicians of being liars, described Gordon Brown as "easily the most boring political interviewee", said of John Prescott, "you can't understand a bloody word he says", and called Peter Mandelson "a man they, I think probably all, detest".
At Mr Grade's behest, the director general commissioned a report from his deputy, Mark Byford, who swiftly concluded that Mr Humphrys' comments were "inappropriate and misguided", but not a sacking offence.
Mr Thompson denied Mr Kampfner's claim that he had initially been minded to sack Mr Humphrys, but changed his mind. "The New Statesman says that on the Monday I 'changed my mind' about sacking John Humphrys once I'd seen the press reaction to the story. Completely untrue - in fact a straightforward lie, I hadn't reached any conclusion at all at that point," Mr Thompson said.
He added: "The New Statesman claims that 'instructions' have been issued from the top of the BBC to 'do anything to win back the favour of ministers and do nothing to offend'. Untrue - and preposterous."
Mr Kampfner said yesterday: "I stand fully behind my story in each and every detail. I'm confident both of the quantity and the quality of my sources. I maintain that pressure was applied to get rid of Humphrys.
"It's untrue to suggest that I'm accusing the BBC of political bias, which I'm not. I'm saying that post-Hutton a climate of extreme risk aversion and of deference to authority has been inculcated at the BBC, whatever and whoever that authority may be."Reuse content