Hm, from my very brief experience with TOAW3 PBEM it looks a bit like that that feature should be used with caution (or at least not be believed at all times). The first turn from Antoni arrived late night, I just openend it to watch the playback and turn start reports, saved and closed it, opened it again to play it next day, and already Antoni did get a cheating report. Turn three I just opened it, played and closed it, all in one session, and apparantely there still was a report.
Maybe the game is confused because we are on different versions ... (v. .14 vs. v. .17)