This is not true for Android. Some OEMs might ship a version of Android that is tied to a single app store (e.g., Kindle Fire), but I'm quite certain that vanilla Android can install any old .apk from any source.
Case in point: Google Wallet.
The openness of Google, nexus, and android is a big selling point for me.
I've got mobile broadband in my laptop. Imagine if the provider of that service would have a say over what programs I could run on my laptop. Very strange.
Video game consoles are similar - MS won't allow you access to the Xbox Live service if you've modded your hardware or installed different firmware.
Verizon doesn't care what you do with your phone, but they say that you can't get their cell phone service unless you run the device the way they want you to.