Proof of Free Offer

We signed up on X day. It was installed a few days later on day Y. Then we receive an email which I copied and posted relevant info below. We took the bait and redeemed the offer, yet were charged for the item. I have been calling and chatting with agents since receiving the first bill that it showed up on to dispute the charge. Months later I still am told no offer exists, we did not redeem in time because they are using the sign up date and not the activation date, and it will be adjusted in the next bill. All this is said in one call. How are we out of date if you just said you have no knowledge of any deal offered? I say I have an email, yet there is no way to prove it's sitting in my inbox right now to the rep on the phone. What are my options? Do I go to arbitration over a movie charge? Seems like this could have and should have been resolved by now. 

From: AT&T  

Now that your DIRECTV service from AT&T has been installed, its time to let the fun begin. Rent any DIRECTV CINEMA ® movie within 14 days after installation and its on us!