In a recent publication, Experimentally Faking the Violation of Bell’s Inequalities (Gerhardt 2011) (arXiv version), the statistics of quantum mechanics is faked using classical light sources. But if it is possible for physicists to fake an experiment to imitate QM, how can we be sure that nature doesn't do the same trick on us? Can it be that QM is a fake, and in the end QM turns out to be an artifact of our imperfect measurement devices?
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.
The so-called "conspiracy" variant of the idea of superdeterminism implies that nature is indeed effectively "faking" quantum statistics. But as John Rennie points out, this is simply an interpretation, not a true alternate theory, so it's pretty entirely a philosophical rather than physical question.
We can't be 100% sure that quantum mechanics is exact until we are able to do a quantum computation in a real system that would be impossible to perform on a classical computer roughly of size the universe. This looks like it is possible, there is no indication that quantum mechanics is only approximate, and there is no known classical theory which limits to quantum mechanics for small systems, but becomes something else for large ones.
But our tests of quantum mechanics are limited to a certain extent by our ability to compute predictions of the theory. By definition, we cannot predict the behavior of a quantum mechanical system which takes exponential resources, because the computation is too big. We must resort to approximations which might disguise a failure of the theory. So while it is unlikely, it is possible that nature is not fundamentally quantum mechanical, and that we just have not seen the breakdown of QM yet.
This type of statement is predictive--- it requires that a quantum computer will have mysterious unaccounted for sources of decoherence which are not due to known interactions, but which are fundamentally due to the breakdown of quantum mechanics. If a quantum computer is built which can regularly factor 100,000 digit numbers, this is good enough to establish that our universe is not classical down below, because such a feat would require too big a classical computer to realistically implement inside our universe, were it classical.