The 1950 ish console my parents had did pick up the local
AM station with the radio off. There was no long antenna.

I'm curious as to what the mechanism was...

The station was located bout 3/4 of a mile away and the
console was all tube with a transformer that fed the speaker.

By "mechanism", I meant what was going on electrically. How was the signal
picked up, demodulated, and fed to the speaker at sufficient level to be
audible?