The OS was relevant if your BBS software was limited to a single simultaneous user, like many of the early DOS BBSes. The late 80's "PCBoard" BBSes I'm familiar with needed one PC per user, plus a file server with Netware.
Ok, but that's just the vehicle, it is the BBS software that does the works. And even in the 80's there were ways to run multiple instances of 'single user' BBSs on one box, for instance (dare I say it...) OS/2 and TV.