The producer was just one of the fictional characters added to the movie, but who never existed in the real story.
And their Iranian maid who "escaped" to Iraq at the end was another fake character. (The Taylors' real maid was from the Philippines, and she did not go to Iraq.)
IMO, there was far too much bogus nonsense added to the movie for them to even pretend it was "based on" a true story. In Argo, there was very little resemblance to the historical events.