yes, it was that the phone was saving notifications to a database, because the notification history feature was not disabled by the user. but that affects non-push notifications too, and it only becomes a problem when your phone is compromised (malware, including police malware)

but if you don’t trust your phone with not leaking your notifications, you shouldn’t trust it not leak what you typed in and what you watch on it either, because the operating system has access to all of these too. in that case you are looking for a better phone brand, maybe even a custom rom that’s known for privacy