The recruiter did mean UNIX-like systems. There exists no useful set of experience which is common among pedantically defined "UNIX" and which excludes UNIX-like systems. The pedantic definition-lawyer type responses you've gotten are absurd.

A role might specifically require extensive AIX experience in particular -- and if it did you would say you needed "AIX experience" -- never some vague umbrella family of "UNIX experience."

It is entirely unbelievable that the requirements for this role would exclude your experience. Doubly so as they're recruiting from interns. Triply so if you know anything about Facebook engineering teams. "Production Engineer?" "Frontend Engineer?" At Facebook? Yeah, those teams run Linux.

ps: The folks telling you not to language lawyer are correct. But your initial assumption that the recruiter had made a dumb mistake was also correct.