Earlier: one PC per user, shared file system using a Novell network.
Later: multitasking OS (Desqview, OS/2) or BBS software that natively supported multiple users (like MajorBBS.)
I ran a BBS on an Amiga for a while. The OS natively supported multitasking, but I only had one line. At least I could log in the same time as a user...
The older brother of a friend of mine in the 90s was the co-sysop of one of Sweden's largest "elite" BBSes at the time, Farout BBS. I got to tag along to the sysop's apartment once and see the setup, which was an Amiga 2000 with 3 active nodes and available serial ports for a total of 7 nodes, though the sysop hadn't gotten around to get more telephone lines wired to his apartment.
awesome! getting more phone lines into a residence could be a pain. I knew a guy who had an 8 line BBS in his (parents', actually) basement. Getting more was difficult because they were "out of facilities" and he had to move it to an office.
> It's a wild misunderstanding of how BBSes worked.
That's quite the assumption.
There were a lot of different BBS hosting programs. They wildly varied in what they supported and how they were implemented. Further even within a given piece of software the ways you could configure them and the consequences also varied. Even if a given software supported concurrent users on a single PC for various reasons a BBS might choose not to host that way.
That said, I have no idea how a multi-node BBS would work, in terms of keeping state synchronized.