When I was younger, I connected via 56k modem over the PBX at my parents' shop. My connection speeds topped out at 33.6k.

Under the hood, V.90 (the standard for 56k modems) expects that there's only a single digital-to-analog conversion, seen from the ISP's side. The line down from the ISP to the consumer is digital PCM until the last mile. In the opposite direction from the consumer back to the ISP, analog trellis modulation is still used. This is why you still typically only see 33.6k upload speeds on a V.90 modem.

Many PBXes will introduce an additional analog-to-digital conversion in the unit itself, before converting back to analog and putting the signal back on the wire to the street. V.90 can't tolerate that extra conversion, so a connection at 56k speeds fails, and the modem backs down to V.34 / 33.6k, which is perfectly usable on a fully analog line.