I think you remember correctly! A lot of the BBS software would just show what the current user was doing as if it was their screen. I believe from there you could start a chat as the sysop and interact with them, else you kinda just watched.

The few times I ran one (was a sysop on a few, but remotely), I was always a little creeped out that I could see people typing messages, etc. Felt like invading their privacy.