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.
As far as well funded corporations, I don't think it would go to a jury unless they want to defend it at all costs. If it gets passed a dismissal motion, it will probably be settled. Most corporations don't want bad press that comes with a trial. They are afraid of juries. Most plaintiffs will be happy to move on with a settlement. Less time and less expenses. I'd give the scenarios and let the client decide.
Personally, I think whoever is asking for passwords is just asking for it. If I'm hiring for my business, I'm not going to ask for that stuff, but I would have a no-facebook/twitter policy on company time.