There is the primer anvil with priming compound between the anvil and the primer cup. It takes a lot of force to punch out a primer and the de-capping pin has a small diameter. Therefore a lot of force per unit of area will be applied and there is no way that the anvil will not be deformed and priming compound not displaced.
A deformed anvil would not necessarily be a problem, as long as they are still in the primer cup when you re-prime with them. When I looked at live-deprimed primers under magnification, I could not see any deformation. As to priming compound displacement, if it does not fall from the cup, there is likewise no problem. "Pre-stressing" the primer compound (slightly displacing), by seating the primer further than flush and slightly flattening them has been a technique for improving accuracy for years.