...that throws a wrench into the scientific method?
Now, there's a clear thought! lol!!
so your question differentiates between what is real and what is physical.
Hmm. If that's the way you think, you should go post your question in the religion or philosophy section, not Physics.
There's one or two of us here that would disagree with your concept that the physical is not real. Maybe even three.
So, if I may rephrase your question:
Is the Heisenberg Uncertainty Principle a result of imperfect observations on imperfect real systems or do we believe it is a inherent property of reality?
And the answer:
It is an expression derived from the mathematics of Quantum Mechanics - there are certain sets of pairs of "operators" (equivalent to "properties" in classical mechanics) that do not commute. That basically means you can not solve the math for both of them exactly at the same time (at the same space-time point). It is an inherent property of reality - just as incomplete information is. There is also experimental error, which results in a different type of uncertainty.