I didn't read the title that way. You can have a (heuristic) solver that finds solutions to some instances of an NP-hard problem in reasonable time. That's not the same as claiming to have an algorithm that, in the strict theoretical CS sense, would solve that problem (i.e. all instances of it) in polynomial time. The latter claim would be highly suspicious by default; the former need not be, as it doesn't imply anything extraordinary.

Quote from OP in another comment:

> I think a better way to phrase it is that we are writing a solver for a reasonable subset of inputs to an NP-hard problem.