I just found something!
How to manage Windows 10 notification and upgrade options
https://support.microsoft.com/en-us/kb/3080351
It talked about how to modify it by computer configuration -- I had no idea what that was, but google told me it was gpedit (from RUN).
The path they gave was Computer Configuration/Policies/Administrative Templates and further... I found it but without the "Policies" entry.
Further down it said how to disable it via the registry. I went there and it was already disabled. Not sure if I had done it earlier, or if the group policy ended up setting it, but who cares, it's done.
They also had a registry key to disable the notification icon, but I don't know if you're s'posed to add a whole folder and a variable in it, so I skipped that.