Don't pretend to yourself it can't happen to you or for that matter you have never made a serious stupid error. Perhaps you were lucky and it didn't bite you that time. I have been lucky and I hate that fact.
You can project and pontificate all you want if it makes you feel better, but I am here to tell you that not once in 20 years have I ever, even once had anything even remotely like that happen / almost happen.
The person on the sharp end of my rope is not coming off belay until I am 100% sure, double checked by visual or extra inquiry that is what they intend. When it's me on the end, same drill. You STAY on belay until you have proof positive something else is requested. You don't leave the anchors under someone else's control until you have proof positive said control is ready.
You sound like someone who got caught drinking and driving trying to claim "everyone does it". No, they don't.
Scary. Especially if one of the children WAS the belayer. Both mine (12 and 14) belay me but they know that 'off belay' is the only time to take me off belay. That only happens when I'm clipped to the bolts/chains, etc. and they respond with 'belay off'.
Maybe my newness to the sport is showing, but how do you clean gear and expect to be lowered? If you're being lowered that happens right when you top out ('Got me?', 'Yup'). Was he getting lowered using the bolts/chains? If someone was cleaning gear I would also assume they were going to rappel, since you're not supposed to lower from the bolts/chains. But I would still wait for the cue to take them off belay. Seems like following standard protocol would have prevented this. I guess if there are walk off options that could happen, but even then the 'belay off' still applies.
I always do the coz grab, every time, even in the gym. I just can't bring myself to weight a rope without still being anchored or at least having a hand on the other side. When belaying, when the leader wants to clean the anchor and rap I leave the rope in the device with some slack until I absolutely know he / she is rapping instead of lowering.