> several 56k baud modems

These were almost definitely 8k baud.

Yes, because at that time, a modem didn't actually talk to a modem over a switched analog line. Instead, line cards digitized the analog phone signal, the digital stream was then routed through the telecom network, and the converted back to analog. So the analog path was actually two short segments. The line cards digitized at 8kHz (enough for 4kHz analog bandwidth), using a logarithmic mapping (u-law? a-law?), and they managed to get 7 bits reliably through the two conversions.

ISDN essentially moved that line card into the consumer's phone. So ISDN "modems" talked directly digital, and got to 64kbit/s.

In case anyone else is curious, since this is something I was always confused about until I looked it up just now:

"Baud rate" refers to the symbol rate, that is the number of pulses of the analog signal per second. A signal that has two voltage states can convey two bits of information per symbol.

"Bit rate" refers to the amount of digital data conveyed. If there are two states per symbol, then the baud rate and bit rate are equivalent. 56K modems used 7 bits per symbol, so the bit rate was 7x the baud rate.