Everyone can use the same physics (general relativity) and everyone concludes that the clock on the surface runs faster than the clock at the center using that physics—including the people in those positions.
The laws of physics being the same for everyone does not mean everyone will have the same potential any more than it would mean everyone feels the same acceleration or everyone is the same distance from some given mass. The physics that everyone uses can be considered:
while different observers have different values of U.
I do, however, agree with you to an extent about the event horizon. Because Schwarzschild was the first to make an exact solution to GR and his metric broke down at the event horizon many people took the horizon to be a kind of physical boundary in space. This is not really the case with GR, but just an effect of Schwarzschild coordinates. In other words: GR doesn't break down at the horizon, Schwarzschild's metric does (because it's static).
~modest
