Legally you're correct, but bartenders don't exactly have the resources or legal authority to take people's keys or drive them home and put them to bed.

Dram shops laws establish liability in scenarios like this and as a rule, they're very old and haven't been updated in forever (think like prohibition). Many places they establish liability even when someone is responsibly served and later continues drinking.

I hate them. Legal liability for other people's actions should not exist.