I like how many comments are left by people who think they know that this story is "impossible" because "it doesn't work like that".
Sure it doesn't work like that--now. But back then is a different story; in the 1970s, it most assuredly did work like that.
A modern modem uses all kinds of sophisticated technology to establish and maintain a data connection. It's necessary because the typical 56k modem is transmitting much more data than the typical phone line is designed to carry, and it's doing it by encoding data into multiple states.
The typical "analog" telephone line has a bandwidth of about 4kHz. That's not a really wide bandwidth, but it's about equivalent to the frequency bandwidth of the human voice, and it's all you need in order to understand what the other person is saying. (In fact, it could be even lower, but the speech would sound distorted, and some people would have trouble understanding what was being said.)
A 300 baud modem doesn't tax the bandwidth of a typical "analog" telephone line. (I put it in quotes because the modern telephone system is only analog as far as the switch at the telephone exchange; there the signal is converted to digital, and it stays that way until it gets to the exchange that the other telephone is connected to.) "Baud" refers to the rate at which the connection changes states; a 300 baud modem changes states 300 times per second. It doesn't quite mean 300 bits per second, but in the case of early modems they are approximately equivalent measures.
Where a telephone line can hadle--theoretically--4,000 baud*, a 300 baud modem transmits 300 bits per second. (More or less.)
I explain all this to put into perspective how low-tech a 300 baud modem is. It transmits data at less than 1/10th the theoretical maximum of the data channel; there is no need for complex error detection or correction.
And, in fact, such things weren't invented at the time this story takes place.
So for guys like me--who got into computers at the tail end of the "dinosaur era" of them--we can understand how playing "Freebird" on a data cassette drive connected directly to a freaking modem could crash a database. Guys who didn't get into computing until cassette decks and acoustic modems went the way of the dodo, they think it's "impossible".
Sure it is. Now. You're welcome.
*The interesting thing is that a 56k modem is actually a 4,000 baud modem. The phone line can only handle 4,000 baud, so the 56k modem encodes data such that it squeezes a throughput of 56k from 4,000 baud...but now I'm just confusing things for people not educated in communications theory. Which is why this comment is a footnote and not in the paragraph....