That's very unlikely to be true in general, as the proofs that a problem lives in NP usually have a very high signal-to-noise ratio -- i.e. in order to prove that solving this problem is at least as hard as solving an arbitrary boolean circuit, we need to find a subset of the problem which behaves like wires and boolean gates do, and the resulting "circuits" are very heavily structured.
In own research (inverse problems related to signal recovery), I've noticed that a lot of NP-hard problems are actually easily solvable given that the data has some kind of structure to it. I know very little about computational complexity theory, but I've read some papers describing how there is often a phase transition where a high SNR puts the problem in P territory, but a sufficiently low SNR moves the problem moves to NP territory (but it's still solvable). Beyond the phase transition, a solution is information theoretically impossible. I wonder if most of these real world TSP problems actually lie in P, but I don't know how one would go about showing that. (I haven't performed a literature search, but I wouldn't be surprised if someone has already demonstrated this.)