Was it not actually instant?

My recollection from the 80's was you switch the channel (physically) and it's... switched!

So was there some magical latency there that I just couldn't perceive, or are the "near instant" reports talking about some other type of TV? Or something else?

Change was instant, took a frame or two for all the sync, gain, etc to settle.

There absolutely was some latency, about 13ms worth, because it had to wait for the next field to start so it could properly synchronize and start drawing. But you'd never notice that yourself.

There was a few ms of latency but you couldn't actually perceive it unless you used a slow motion camera or something.

Yeah, I think that video appears to still have some digital delay. Perhaps something related to the satellite receiver decoding in that example.