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.
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.