And I'm still not saying 'good on ya' to the GA because s/he didn't know who would/wouldn't & made it sound as those who didn't would automatically get charged.
I get why s/he did it, but think s/he was misleading & not appropriate. Also, was the flight late coming in? Was the turn shorter? Given most flights board 30 minutes early, was there a reason to think that that wouldn't be enough time to put stuff in overhead - or for the stragglers (which is the norm; they usually get their stuff gate-checked & on all the flights I've been on we've still managed to take-off on time). I get pro-active. I'm a bit leery of how pro-active is applied, and think saying folk would automatically get charged is not the way to do it.
My understanding is that the push-back is not something the GA decides, but ATC (or is that ground control?). Whichever - GA closes the door & after that, GA is NOT responsible for push-back.