Not Limited to US
I've heard this same BS from (in alphabetical order): AA, DL, NW, UA and US
But it's always been an admonition and nobody's denied boarding for me (and lucky for them!)
We could go on about what could've/should've been done at the airport, but it's "spilled milk." The points above are all good, but want to emphasize to definitely report this to the DOT, it will be a nick against US' DOT complaint report record.
Since this was an employee based problem, I would also detail the conversation. It's one thing to be dumb and another to be dumb and argumentative. This employee should have asked for a supervisor to step in (and really your daughter should have demanded it) and weigh in. It appears this employee is on a power trip. I'd love to see them use their power while they are standing in an unemployment line. Unfortunately Illinois pays a nice unemployment check, too bad they don't live in Arizona.
You might even take it to the next level and copy in their union after the fact. Of course they will blame the Little Mussolini's act on lack of training and won't take into account their flawed personality. But it's always a good thing to slap the union upside their head so they can see the problems that are compounded by rotten employees when it is piled on top of poor management. <<<< which is more poor management through hiring rotten people like this Little Mussolini.