How can we be sure that nature isn't "faking" quantum statistics?

I'm not sure it makes sense to ask if Nature is "imitating" Quantum Mechanics.

Quantum mechanics is a mathematical model that gives predictions that are in excellent, well so far perfect, agreement with what we actually see.

I guess the question is whether QM is just a good approximation to the real world or whether it's an exact description of the real world. We'll never be able to prove it's an exact description, but someday someone may find an experiment where QM gives the wrong answers. If so this would prove it's just an excellent approximation.