The amount of ppl in this thread seemingly suggesting that it's ok for a salaried employee to actively force paying customer to not do what they are perfectly entitled to do (board as close to 15 mins cut-off as they feel like, for any reason they want whatsoever) so that said salaried employee can go home earlier is amazing.
I welcome OP to ask for the GA's name and lodge a complaint with UA management, naming GA and highlighting that this is wholly inappropriate.
This is certainly what I would do.