I think he thinks HE had to store the information, and if he isn't the one storing it, it's anonymous.

Except, on Android, you can also do it where only google stores the information and he doesn't have to store any. And there are no user name or passwords or accounts involved to listen to specific channels like he claims.

You can collect this information, and you'd be able to write a more custom push service, but it isn't needed at all, but Google and Apple will always know who is getting the messages.

You don't even need to audit a closed source app to know that Apple knows which devices its sending pushes to. It works because they know.

It makes me suspect they’re not talking about the stock systems OEMs ship.

The developers of GrapheneOS, an independent, security-oriented Android distribution are probably not only talking about stock OEM Android. What they're saying is true about stock OEM android though.

That's a separate issue from whether users are forced to get all their software from a specific source, which is also separate from whether users will actually use other sources when given the option.

On Android, developers can offer users a way to install an app that isn't easily traced to their identity and on iOS they can't. Furthermore, an Android app can be both on the Play store and available from other sources; there's no exclusivity.