BBSes were pre-public internet, not part of the internet. The connected ones were a separate network in and of themselves. I ran a WWIV BBS in the late 80s to early 90s that had its own networking system allowing communication, and even file sharing between instances. It was pretty sophisticated for the time, but hella slow over my 14.4k modem.
WWIV did migrate to using the internet for connection, and maybe others did as well. Perhaps that’s what you were considering with this comment?
Maybe take it up with his boss? I really can’t see the restaurant caring one way or another, as long as the shift is covered by someone qualified to do the job.