Facebook hires (or at minimum, interviews) hundreds of PE's a year, there's no way this sort of miscommunication isn't sorted out in the average case.
I might be wrong, but as far as I know PE's are recruited to have SysAdmin expertise as well. It's clear that the resume didn't reflect that as well as it should if this was even being asked.
You're right about the full-time PE role but this is an intern role - how much production fire-extinguishing/sysadmin experience could they expect a student to have?
It's definitely plausible! I met a guy who had gotten a PE intern offer from FB. He said he had an systems internship at a trading company where he did automation and and infrastructure.
I wouldn't know for certain but I'd think they'd be looking for experience with scripting languages and deployment systems as well.
I might be wrong, but as far as I know PE's are recruited to have SysAdmin expertise as well. It's clear that the resume didn't reflect that as well as it should if this was even being asked.