I remain skeptical. NC=P? is still an open conjecture, so there could be problems which are decidable in P, but only when using a polynomial number of processors or superpolynomial on a single processor, but polynomial on a polynomial number of processors. Furthermore, the amortized complexity of common instances could turn out to be tractable on average (e.g., random 3-SAT instances are tractable unless they fall in a very narrow region where the ratio of clauses to variables is ~4.25, but NP-complete in the worst case).