I figured you were right, so I just signed up for prime.. through the app, and it didn't use the play store payment system, so Google isn't taking a cut.
Again, I have no idea what is possible on the Apple version, but I have subscriptions on other apps that go through the play store payment system. I'm not an expert on app store policies for payments, but I don't use any other apps that have subscription payment that don't go through the play store. I have a LastPass subscription which I purchased through their website, specifically because you have to go through the play store if you get it through the app.
Again, I have no idea what is possible on the Apple version, but I have subscriptions on other apps that go through the play store payment system. I'm not an expert on app store policies for payments, but I don't use any other apps that have subscription payment that don't go through the play store. I have a LastPass subscription which I purchased through their website, specifically because you have to go through the play store if you get it through the app.