I agree with you. I have also seen that "United First International/UGS" sign at LAX, and I read it to mean either United First International pax OR UGS pax may use that line. If it meant "UGS pax who are flying F," then there should be another line for "UGS pax who are flying C or Y," with "should" being the operative word.

Now, you didn't mention how many agents were on duty at the time, but based on how thinly staffed the Elite Check-in area at LAX is, I would speculate that the agent checking you in had to handle the other line too, and that's probably why all those people were upset. It wasn't so much you using that line, as it was their agent having to stop working their line in order to handle your check-in.