I'm no expert on the matter, but I've developed and published multiple Android apps to the Play Store. Some of those apps have needed Google Play Services APIs. Google has also been actively making moves to lock down control and offering things like the Play Integrity API that some apps use.

By your phrasing, it sounds like you're implying my understanding is wrong somehow. If so, what am I missing?

I'm not the commenter but this is my experience in about 10% or so of cases. I've been running a network audit of baby tracking apps and the information they phone home with (results are pretty Orwellian so far) and a few of the apps have been virtually impossible to emulate without an active Google Play account that is verified against Google's servers.