I agree it is confusing. In particular, the controllerUserInteractionEnabled flag on GCEventViewController does not seem to do anything different whether I set it to true or false. Does it only affect "real" game controllers and not the Siri Remote?
In any case, here is how I solved this, I am not sure if it is the right way. I ended up ignoring the GCControllercontrollerPausedHandler flag, I don't set it to anything. I am not sure how it works with the other ways of reading the Pause/Play button.
Instead, I use GCEventViewController and pressesBegan:withEvent. Check the pressType for UIPressTypeMenu to handle your pause screen. I have found that when my GCEventViewController is the firstResponder, then the button will not pull out of the app to the home screen. It only does that when the GCEventViewController is NOT the first responder.
What I don't know is how to handle the situation if the user WANTS to exit the app to the home screen. I know that I can set the firstResponder to something else, and then the Menu button will leave the app, but from a UI perspective, you'd want the user to select a button on the pause screen that says "leave app" or something, then manually leave the app for the home screen rather than have them press MENU. I haven't found out how to do that yet. I guess you could put up text that says "press MENU to leave app" or something once that option is highlighted.