Wow... You have to fight it.
In a case like this I get upset, but keep it in controll. Do not budge. Tell them that you thought they were a company of integrity, and you appreciated their service, and feel like they cheated you. If that does not work with the CSR, ask for their manager, and get in their face a little. Never cuss or degrade them on any level. You will get nothing from them if you do that.
I have in been a situation like this with my Internet provider. The same thing happened, where I caccelled the day after my contract expired on my "special rate", and I still got a bill for that month for a full month of internet at rate of $29. I called back explained my situation, and even the manger would not budge. I called back the next day, and told a different manager, that I had recorded the phone conversation that the CSR and I had when I cancelled the service, and she clearly stated that I would not get charged for any internet at the regular rate. That got his attention, and he reversed the charges!
I friend of mine has even used the line "My father is a lawyer and would have a field day with this. It won't cost me a dollar because he will not charge his own kids, but it could cost you thousands, and get you in the news"! This has worked for him on more than one occasion. I don't believe I would go this far.