That's broadly true, but I suspect it's a bit more difficult, at least on Android. Updating the operating system involves the company making the device (at least it used to, I'm not sure if that is changing), and it's much slower to roll out than an app update. I don't know if the extra bits like 'Google Play Services' have the necessary access to e.g. read private data from a messaging app.

As the OP is pointing out, the simple alignment of one platform with one app store is also a bit blurred. Neither Google nor Amazon control Windows. You can install the Amazon store on other Android devices. No doubt Samsung (and some other manufacturers) are trying to do their own marketplaces. And it's conceivable that in the future, they're forced to allow more competition (e.g. something like Steam for phones).