No, that's not the case. The user only gets a prompt if the app requests permissions. The user doesn't get a prompt if all the app does is check for authorisation – the state is returned to the app as UNAuthorizationStatus.notDetermined without showing a prompt.
If an app prompts the user for permission to send notifications as soon as it starts up, then it's the app's fault. It's been known to be bad practice (and counter-productive) for many years.