Interesting. So, basically, it sounds like you had some dial-out modems hooked up, and some kind of database of other BBS numbers, kind of like a routing table, except you basically offloaded the actual routing to the phone company? Then, you could call out to the other BBS and switch the user's display to show the external BBS rather than yours?
If so, that's an interesting idea, but it kind of sounds like a good way for your users to run your phone bill up rather than theirs, while possibly not even engaging with your BBS at all. (For those who aren't familiar, back in the BBS days, you had to actually pay for "long distance" phone calls. And, "long distance" often wasn't very far away.)
Do I have it right, or was it something different?
Not exactly. An actual packet network, so the connections would be multiplexed just as if you used an IP connection, and routed it at like over a dedicated network. The modem part is an implementation detail.
In terms of cost, it was normal at the time to charge per minute fees for services on the big online services, so enabling remote services multiplexed over a network like that would be an opportunity for BBS operators to federate into a bigger network and gain revenue by charging for services, and start out without having the traffic to justify a fixed line.
But obviously, just like the big online services, that model became unviable the moment the internet went mainstream.
Yes, it was basically re-inventing IP for no good reason because lack of internet access meant lack of info about what already existed...
When I, a few years later, got an internet connection and started reading the relevant ISPs, it was pretty annoying to see what had already existed.