Yes, they do, but my parent was saying that his location was worse, with wifi off in the last week, than it was before, also with wifi off. Apple Maps being up and down won't affect your location accuracy if your wifi is off.

(My parent was almost certainly incorrect. Having wifi off has always made location pretty bad on iPhones.)

I think your memory is accurate. When I've had WiFi turned off in the past I'll sometimes get a pop-up message on my iPhone suggesting turning WiFi to improve location accuracy.