When the incoming flight is on UA, they'd have easier access to information about when the passenger is expected to arrive, but otherwise I don't know how much of a difference it makes. I'll withhold judgment on how surprised I am until we find out whether your friend arrived at T-29 or T-11, but the GA's statement doesn't really make a lot of sense. The reason for the 30 minute cutoff isn't to prevent people from arriving without their luggage; it's to give UA time to get their luggage off of the plane when they no-show.

That said, the positive passenger-bag match rule is widely misunderstood. It's entirely possible that the agent could have boarded your friend but didn't know it was allowed.

Definitely could have been worse. ^