Private security, bouncers, etc. do not have the legitimization of the force of state behind them. Police are "allowed" to be violent because it is the state being violent, not a privately employed individual. That changes the ballgame significantly.
Should it? A totally different question. Does it? Incontrovertible.
I agree that this is the case, at least in the mindset of everyone involved.
But then how do we reconcile the fact that, at least in common law societies, it is not the case de jurie? If the laws surrounding this are different from the reality, haven't we lost our claim to be a society of laws and not of men?
That's a big question, isn't it.. and I think in part, the answer is yes. When we make exceptions to the law, even if convenient at the time, that's exactly what we lose. If we make exception after exception until the law is a watered down toothless goat, well...
Should it? A totally different question. Does it? Incontrovertible.