Wouldn't a simple solution to the question of cheating, be to simply check the scenario files? If both players are using one of the default scenarios that are installed with the game , then obviously no changes have occured and your opponent is not cheating, if on the other hand, the opponent in question has insisted on supplying the scenario files, that would seem quite suspicous. As others have said, you need some proof, rather than just a accusation or feeling you have been cheated.
The OP is suggesting that the gamefiles have been hacked. That would occur after the game started, so reviewing the scenario files would not reveal anything.
I agree with SML - OP needs to post far more data for anyone to have an opinion. Combat results with dates.
I also agree with vettim89, I find it odd that the opponent refused to exchange passwords.
Not necessarily odd, I foolishly used a password that I use for a number of sites as my PBEM password. I'm not planning on exchanging it until I used the password changer in the beta at the end of the game.
That said, the combat results give by the OP are very uncommon, but whether it's 'cheated' uncommon or 'Completely different skill levels' uncommon is impossible to say from the info we have.