L.A. FITNESS Cancelled Policy but still got billed - Would not give refund Mesa, Arizona

On 1/5/2010 I called L.A. Fitness to inquire on canceling mine and my girlfriends membership that gets billed to my bank account every month. I spoke to Josh who said they only except cancellations via written request mailed to their Processing center in CA. He then stated and so did the form I printed from the web site that they need to receive this request 7 days before the next billing to avoid future billing. Josh assured me that I would not receive another bill if mailed that day so I mailed it. I mailed it on the 5^th and my billing is on the 14^th. So today on the 15^th I saw the charges for a total of $70 and called them and spoke to Josh again. He said they had not yet received my request and there was nothing they could do but I should mail it again. He said I see here you did call on 1/5/10 to cancel but there was nothing he could do. So I asked for the customer service number and he gave me 949-255-7200 and I spoke to Zanoni who looked up my account and said the same thing. She said to re-mail it and I asked for a fax in which she said only by mail will be accepted. I asked her to refund my money due to the fact they Cleary have documented I requested to cancel on 1/5 and she said she could not. She then said I can go ahead and cancel your account to help you out this way I would not have to mail it again. While this was very kind of her it makes me wonder why they didnt just do that the first time I called. Do they anticipate the Lost factor to make them more money? I still feel they owe me a refund of my $70.