this is one of a number of challenges confronting the press in this age of disinformation and propaganda, including the "bias to neutrality" and toothlessness of media standards law, and there may be no easy answers to any of them - sadly, the press shows little signs of even trying.
I think whilst you have to report what Trump says it is irresponsible to put it in the headline considering how casually people digest news.
Therein the problem. Same with Farage, Badenoch, Rowling and whoever else. They all know their words will be reported, and that most of the audience will read the words and not the context.
bury the words in the article and folks will have to get context to read them. l "x makes claims/statement about y" as a headline doesn't propagate any falsehoods.