Then, a few minutes or an hour after the meeting, in both the versions of the situation Peter comes back to me and says: "Sorry, changed my mind. Could you do that/ help me?".
Just respond (in a perfectly neutral tone with no hint or sarcasm or snark and no emphasis on any words): "Sure. Just talk to [your boss] and let me know what work can be delayed so that I can help you with the work that you agreed to do. It's unfortunate that you didn't realize this sooner when we were planning."