When bees become stressed they may actually attack the queen or may surround her to protect her. I think in my case the latter happened. beequick causes the bees to set off their alarm pheromone--it's a hive invasion.
I don't know If I could prove your first point but from my experiences, when bees become stressed, they will ball the queen. I have seen this first hand doing removals.
I had one removal that was in a dormer over a window. I opened the dormer to expose the hive and right off saw bees balling a queen. Not sure why really, were they stressed or just 86ing that queen, but I did not find another one and thought it odd they were killing the only queen in this rather new hive. I chalked it up to stress.
I've seen them balling and stinging queens on other removals as well.
I have never experienced bees setting off alarm pheromone after applying beequick, I'm sorry but I have to disagree with your statement on this. I have used beequick on too many hives to remember, this is where my experience with beequick comes from and also from using it on fume boards to extract honey.