So if she thinks it's weird that he hasn't said hi, why wouldn't she just say "hi"? There's literally a million other polite and innocuous things to say besides "why do you look angry." Just the fact that they work together means they have to communicate at some point for their jobs.

it'd be awful to work for a couple of years with a guy who looks angry all the time and hasn't said a word to her.

Who would care? I will never understand why people minding their own business bother other people so much. If she makes the choice to internalize someone else's demeanor and facial expressions that have absolutely zero to do with her, then that's her own insecurities coming through and she should probably look up some therapists.

Except asking why you look angry all the time isn't remotely polite. Not everything needs to be a reference