I wonder if the lawyers have a hand in this. Words like "liar" paint a person in a negative light and could lead to a defamation lawsuit. Whereas pointing out that something is a "falsehood" is inviting a comparison of facts - i.e. inviting Trump to prove he wasn't lying.
That is what I understand; lie implies intent, which is impossibly hard to do. IMO the media is trying to being courteous, even delicate, when it is and should be an all out brawl, when the truth and fact are at stake.
I kind of like the vocabulary they're using. Everybody knows politicians lie, and I don't think that word would have much of an impact. Repeating the term "alternative fact" and using terms like "believes... won't provide any proof" draws attention to just how absurd these particular lies are.
It only draws attention for paying who willing to think critically. Lots of Trump supporters are perfectly content with the notion of "alternative facts."