I think all petcos do it differently, but my petco takes pretty good care of their bettas. They were MUCH worse a year ago, but they have since improved.
I've seen them changing the water in the cups before and they had one bucket with clean water and one to put the dirty water in. They would simply net the betta and keep it in the net while they cleaned the cup.
As long as the bettas are properly taken care of I don't see a problem keeping them in the cups. If proper water changes are done they are fine. You have to remember it is only a temporary home for them.