I think real agents act as though they believe they have free will.

That means that they rate their own decisions to act as determining their actions, and advice from others about how they think they are going to act as being attempts to manipulate them. Another agent encouraging you to behave in a particular way isn't usually evidence you should update on, it's a manipulation attempt - and agents are smart enough to know the difference.

Are there circumstances under which you should update on such evidence? Yes, if the agent is judged to be both knowledgeable and trustworthy - but that is equally true if you employ practically any sensible decision process.

Re: if an agent takes the action that it predicts it will take, it's predictions are true by definition, so any action suffices.

Agents do take the actions they predict they will take - it seems like a matter of fact to me. However, that's not the criteria they use as the basis for making their predictions in the first place. I didn't ever claim it was - such a claim would be very silly.