I corrected one posting in a comment "You basically had to dial the number for your ISP." is of course wrong - direct dialin predated ISPs. A bit of lengthy personal history below about the credibility of this kind of attack for the times.
I was a VAX/VMS sysadmin for a mining company from about 1986 to 1989 and I had one direct dialin line which was a publicly accessible phone number - if anyone had guessed the number they would have been able to get a login prompt.
However, VMS was a very secure operating system, so the line was configured with a number of security features, from memory:
- Only a very small number of password attempts were allowed, with the line being locked out for a random period if they were exceeded.
- Any login failure resulted in immediate printed alert on the secure paper console in the computer room, my screen if I was logged in and an email to me (yes there was email back in those days).
- Terminal sessions through the dial-in line were logged so all incoming keystrokes were recorded.
"War-dialing" was a big deal and the trade magazines were full of tales of people finding that their company had exposed entire banks of phone lines with access to the computer. Whilst VMS could be secured very easily, there was also a time when it shipped with a "system" account with a default password and, even worse, the equally privileged "field"/"service" account which some technicians left enabled. So, finding a phone line that would answer was potentially a big deal in getting access to all kinds of systems.
We also had chains of bulletin-board connections where messages went via a store-and-forward system that could take days to forward messages, depending on volume and how often some people in the chain connected their computer to the next nodes.
If you're interested in hacking tales from that time, check out Clifford Stoll's "The Cuckoo's Egg" about how an astronomer turned sysadmin found an international hacker.
I forgot that I caught our commercial programmer allowing his girlfriend to login through the dialup port. He had sysadmin access and had created a program for her to run a home business generating labels. He didn't know enough to hide the activity by disabling logging on the port. That's my most exciting real hacking story in my entire career.