The difference is that you can have a model that is not precise and which still makes useful predictions. You can't have a proof that's not precise and still proves P=NP.
Note that it is not "the existence of free markets" that is assumed and breaks things, but the existence of free markets with a particular formulation of a particular property. As strictly defined there, weak-form efficiency also allows seems to allow FTL communication.
Either markets are weak-form efficient and P=NP, or markets are not weak-form efficient and P≠NP.