Yes, I already said the background estimation can be wrong. We can check it by defining validation regions outside the signal region and making sure it correctl

Yes, I already said the background estimation can be wrong. We can check it by defining validation regions outside the signal region and making sure it correctly describes the data there (where there is no signal) and assign a conservative systematic uncertainty to cover any differences, but yes it can be wrong. This is a background estimation problem though, not a flaw with hypothesis testing. By the way, the signal region data and background data are collected simultaneously, so there can be no systematic difference in experiment conditions between the two. As for the SM, we are looking for those places where it is incomplete, and to do this we must assume it is complete and look for strong evidence that we are wrong. To date, it doesn't seem like we see though, as far as collider physics is concerned.