It's not either or friend. Professors are subsidized because they are involved in the business of educating young minds. They should be held to a higher standard, including background checks, not only because of those subsidies, but because they are accountable to the "breeders"(I call them parents) of those young minds.
I like the "higher standards" arguement. Most applications ask you if you have ever been arrested or convicted for anything other than a traffic violation. Anyone answering that question should expect a verification would be run. Even more important is to verify the academic credentials on the resume. Again, a background check makes sense. I agree with nothingnew, who wants these guys held to the same standards as the non-academic world. (And yes, I have had background checks run on me as a condition of employment.)