I'm sorry to hear that all your hard work was erased. Unfortunately, ban actions are not reversible. I suspect the primary reason you have not seen a direct response from TA or ATVI in this post is because the enormous volume of similar posts throughout the year to this question.
The justification you provide does not work as an excuse for at least one irrefutable reason: you could have contacted ATVI Support for verification as to the legitimacy of the message you claim to have received. The nature of the message you claim to have received also demonstrates your own lack of prudence: common sense should have dictated that neither the developers, the publishers, nor the network provider (Xbox Live) would have threatened you with action for not playing the game.
Not only is it possible that someone on your friend's list could have sent the message, it is further possible that a former friend sent the message. Still further, it is possible that a "friend of a friend" could have sent the message. Yet further, any player you met previously in a lobby could have sent the message after collaborating with you via voice chat in order to make sure you "inconspicuously" received the invite.
Regardless of how you found yourself in a hacked/modded lobby, the fact is that the investigation process is extremely thorough. If you were issued a temporary ban with your stats reset, consider yourself quite fortunate. That is usually the response to a first time, "mild" case of cheating.
I strongly recommend that you do not participate in cheating in the future. I further suggest that you closely examine who you choose to associate with while playing online games in order to avoid harsher punishment in the future.