His example is good but it's not only a legal distinction. Colloquially I think mixing them up is even worse because while in a legal setting all the parties will know exactly what their own jargon means, to a lay person proof carries a connotation of "being proven and factual" that evidence does not. We all know you might need lots of evidence to prove something, but nobody says "ok so you've got proof but is it enough proof to prove it?" Admittedly the words are synonymous but I would never use them interchangeably if I wanted to be precise. And journalism should be a technical, pedantic field as much as a court of law should be. Instead, news writers like to play with synonyms to sway emotions one way or another. Had they used "proof" in all the above examples over the last two years, some normies might wonder "Ok so it's not proven, but maybe they had some evidence?" And we can't allow that.