Is bacterial resistance really due to mutation?

Easy. Only acquire 1 bacterium. Let it go through mitosis and move some sister cells into another petri dish and start pumping in anti-biotics. If all the sister cells of the original bacterium died, then we know for sure that the original bacterium was not anti-biotic resistant.The problem I see is not that you or your friends cannot think of methods for such an experiment. The problem I see is that you and your friends have trouble understanding the significance of how bacterial genes work or what mitosis really means.This is a problem when communicating in layman's terms. The significance and meanings of concepts are lost.

Actually, going back to your original question, which was how do we know that some kind of change occured, the very fact that you start out with a single bacterium and after it has grown to a culture and at least some of them died as a result of anti-biotics should be enough to show that some kind of change in their genes occured, whether the original bacterium was anti-biotic resistant or not.Sorry for the long sentence. I don't think it's a run-on, though.