I like how she worded that: "I don't think THE PRESIDENT would be that petty, do you?", to which the answer would normally be "no, of course not."

Replace that with "I don't think TRUMP would be that petty, do you?" and she'd look kinda dumb.

Its like if you say "the president is a wise man." it sounds ok. But if you say "Trump is a wise man." it sounds ridiculous even though you're talking about the same person.