In house counsel can "say" that, but do they want to test that in front of a jury? State or Federal? I'll take that case if my client has his facebook settings set to private.
I’m not sure you’d win against a well funded corporation. Corporations don’t have the right to discriminate based on certain well-codified criteria — but they surely DO have a right to vet employees. It’s no slam dunk on your side, either.
Then again, I’m not sure it would ever really get that far.
Side note: if there’s that much risk to the corporation, you have to ask yourself why they’d be willing to take it. My opinion: I think hiring has become such a minefield that employers feel backed into a corner themselves. And rightfully so.