Latency for a 56k modem was 180ms. Latency for a voice call on the same line was _much_ smaller. AFAICT, latency from my games console television to my TV is much higher...

300ms was not unusual on a 56k modem, if my memory serves.

180ms is what I got on WirePlay. The number is burnt into my brain. If the machine wasn't co-located, I can envisage it being a lot higher.

Yes, I believe you, I meant I don't remember what the latency was.

When I accessed the Internet over a "56k" modem connection, my network latency was less than 100 ms, so how could that be possible?

Cable tends to have a higher latency than aDSL. I don't know if that's the tech or just over-subscription on cables part. The trade off is in the bandwidth allowed so people mostly gave up that feature in exchange for enough bandwidth to do other stuff.