The question here is very unclear as you haven't posted the full quote:
"The whole point of push notifications is that the process doesn't need to run for your app to receive messages. See the video tutorial."
This is correct and is indeed the most important point of using push notifications.
It doesn't mean that there aren't cases where you won't receive messages. For example:
- If you throw your phone to the fire then it will not receive messages. Same is true for throwing it down the toilet.
- If you stop the app from the settings page then the app will enter the "STOPPED" state. In that state it will never start until the user explicitly starts it. This is the same as newly installed apps that never ran.
This is very different than regular usage where the OS kills the app. This is also different than killing the app from the recent apps list.
Do note that on some devices killing the app with a swipe also moves the app to the STOPPED state. This is not the correct behavior.