The theory of quantum mechanics is obviously always open to questioning. But a competing theory will have to describe the same behavior that we observe as purely random. We harness these behaviors described by quantum mechanics to create modern silicon based transistors, LED based monitors, street lamps, light bulbs, and all manner of other things including determining the chemical makeup of the sun and other distant and local objects (any kind of spectroscopy).
The wave/particle duality and uncertainty principle is highly supported by repeated and repeatable evidence.
Just because some guys at rutgers have an alternate theory doesn't change that the formulation of quantum theory hasn't fundamentally changed our society through it's direct application.
I believe the evidence makes it clear that determinism is out the window. I have never heard of "Bohmian mechanics" but that does not rule it out either. My point is that it has a LOT of work to do. Simply stating a theory doesn't scrap its opponents. This is the ID argument (not saying you're putting this kind of argument forward).
I'd change your "probably" above to "according to all evidence gathered so far."
Quantum theory is not something that nature must map to. It's a theory constructed out of purely empirical observations of nature. There's a long line of experiments that illustrate the findings.
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