If USF was faced to cancel a contract because they were not able to comply through no fault of their own, they would have a defense to breach of contract based on impossibility, which would allow them to rescind the contract without recourse. So if whatever they found was so egregious that it would prevent them from hiring him in this capacity, they would be fine. If not, he might have a valid argument. Either way, you can sue anyone for anything regardless of right or wrong.
This is, of course, barring any actual legal language that makes the agreement contingent on the results of a background check which if Best Buy has figured out for employment contracts, you'd have to hope the big wig search firm would have been tipped off to the existence of this caveat at some point.