You know...most payroll systems are "accessible by modem" if the modem gets you to the internet so you can remote in to your systems.
But back in '93 ... it probably did go over the phone line in the clear.
Back in the 90's up until the mid-2010's, I dealt with a certain brand of medical office electronic records (ie electronic medical records or EMR) that ran on AIX that was very popular then. The support came with a USRobitics modem that sat on top of the server system to allow the support desk of that EMR company to call into the server for administration. The dial-in user had full admin rights, as it was simply the "root" user. Yea, that root, ya know, "root". And I'll let you guess the password, it only had four letters.
Since my company's product needed root access to finagle a few files living in /etc for it to run, I'd simply go in the client's office, ask to do a simple "site survey" which was mostly to look at the modem for the number, half the time posted on the bottom, or at least do a Sprint ANI to get it, then "good day"ed out. I'd also look for a note with the root password in the rare case it wasn't the default. My own work to install my company's setup took 15-20 minutes, and I was rarely if ever questioned on what I was doing on their precious server.
Whenever there was a need for me to work on my company's software, I had the dial-in access and used it. And certainly, it always occurred to me I was accessing a system I didn't own without the client's specific permission to do so, and could have been violating not a few of HIPAA's concerns. Later that EMR company moved to RedHat Linux, and dial-in access got a -lot- harder but still doable in many cases. It wasn't the only company using a "real" Unix, there was also another company whose EMR ran on SCO. They didn't always have a modem for dial-in support, but I never failed to get the root credentials for my own support use.
Note: "real" Unix, as that's how those companies' support looked at it, AIX and SCO were "real", Linux and *BSDs weren't.