You can put your coat up there. However, when space is tight, as it usually is, the FA has the right to tell you move it.
The notion that an FA will be disciplined or retrained over this is ludicrous. This is standard procedure. I don't think I've ever seen a time when a FA allowed a coat to stay in the bin when juggling things around to try to fit in bags. They move them to the coat closet or stuff them on top of bags once all bags are in place.