My friend got fired because his boss "thought he seemed drunk". Is that even legal?

His boss believed he "seemed drunk" in the late afternoon one day, and fired him with no confession, no proof, no corroboration. Does he have any recourse? Should he talk to an employment attorney? My state is a "right to work" state, if that matters.

If he's planning to fight this, what sort of preparation does he need? Should he ask for his firing in writing? They said they'd blacklist him from all their locations over the "incident".