Sure, in theory operators can just allow anyone to pay the invoive for other people.

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True. I was thinking of when someone quoted or broadcasted notes. If that ought (or maybe already does) bring along a backup of the original note.

That puts the note on more relays.

That is not always the case. Many times clients just create a new note with an nostr:nevent1qqs... reference, meaning the quoted reply note can survive whatever its replying to.

You see this in action when you see a note with a quote reply and it's content is: "This note is not available on any of your relays"

Yeah, I just meant that even broadcasting might lengthen the time the note will exist, as the new relays start counting from the beginning.