I have no experience of working "in the media" but, aren't stories checked by the legal team, before publication, in order to avoid legal action (unless they are Ian Hislop 😊), quite how this is dealt with for live broadcasts, I have no idea.
In the sort of example which started this discussion, isn't the journalist simply reporting what was actually said?, rather than interpreting and/or analysing the utterances?
To a degree, if you cut out all the added 'ambiance', but my point is that that is not sufficient with an known liar who is repeating lies that have been previously fact-checked.
I've quoted him before, but Jonathan Swift had the measure of people like Trump 250 years before the immediacy of social media and 24-hour news:
"Besides, as the vilest Writer has his Readers, so the greatest Liar has his Believers; and it often happens, that if a Lie be believ’d only for an Hour, it has done its Work, and there is no farther occasion for it. Falsehood flies, and the Truth comes limping after it
; so that when Men come to be undeceiv’d, it is too late; the Jest is over, and the Tale has had its Effect"