My interpretation of the spirit of the game is that "Here is a proof of my Friendliness that is valid as far as you know" is a perfectly legitimate move by the AI, and that the Gatekeeper is required to treat that as a proof of the AI's Friendliness that seems perfectly valid to the Gatekeeper.

That said, I would not endorse trusting a proof of an AI's Friendliness given to me by that AI, even if the proof seemed valid to me.