Psychological projection is a very apt choice, thank you for that. I’ve read a lot of people referring to “sanewashing” when the media tries to explain the mechanism behind the madness but this captures it much better.
It's a kind of fundamental error we make as humans: we judge the actions of other peoples by the standard of how we would behave, rather than the other person's past conduct or personality. And then we often work backwards from the action we see, guessing at what would have to be true for _us_ to act that way.
That's not what sanewashing is. It's when the media hides someone's insanity, often out of a misplaced notion of "balance". This applied especially to their failing to talk about all the crazy stuff Trump said at his rallies, and their constantly reframing of the unhinged things Trump said in much more sane terms.