Re: why should it be trusted?

Perhaps it is you who should do so. Showing a problem to be asymptotically Omega(N!) or Omega(N^N) (or Theta of either) is effectively proving it to be NP-hard--that is, it grows in non-polynomial time.

Probelms are not asymptotically Omega(N!) or Omega(N^N). Solutions are. I don't believe anyone has ever proved that an NP-hard problem can not be solved in polynomial time. Not being able to solve a problem in polynomial time with current techniques does not make it unsolvable. MIT people always surprise me.