I personally thought it because of some exposure to that industry / video / AV over the years. But then I looked for some examples to confirm and easily found many.
Aha, interesting, thanks! I had no idea; I'd always thought it was from "master copy" like in, say, a manuscript that is duplicated by hand. (Sure, the life of a mediaeval monk working in a scriptorium was pretty strictly regulated, but I doubt anyone saw them as slaves, exactly.)
Though that Ampex manual isn't all that convincing in this context, IMO. It's about the hardware level, all capacitors and oscillators and stuff, in "master" and "slave" amplifying circuits. That has pretty much nothing at all to do with "master tape" per se; it's more like "master" and "slave" hydraulic cylinders in the clutch or brake system of your car.
Your HN link feels like a much better argument here. (Though I admit I haven't followed any of the links in it yet; going just by the quoted bits in the comment.)
Some decent examples here - https://news.ycombinator.com/item?id=26504086
Googling "Master Slave audio manual" has a bunch of examples. E.g. this manual from 1959 - https://www.worldradiohistory.com/Archive-Catalogs/Ampex/Amp...