There has to be some kind of middle ground here, some kind of way to do it that gives you quick access for transitory things, like email and text messages, but also lets you get back up the stack. Maybe if artificialy adding things to the stack was disabled when you're coming from notifications, but not otherwise?
You would be able to tell if the user had previously used the app, gotten to a state, switched out, then went back to the app to find that state or if the application was pushed to a certain state when it was opened.
Personally though, I would prefer the back button system-wide only. You can easily provide a UI element to take you to the top of the stack (especially since when an app is forced into a state, you only want to get to the top of the stack). Sometimes I even get confused when the back button takes me back a webpage in the browser.
