Credit Card Activation

I live in California, and was offered a credit card over the phone. My family then went on vacation, and while gone the credit card must have come in. I have never had possession of the card, nor activated it (I didn't know it came), but somebody got a hold of it, and was able to charge it up to the limit. I called the company to say I never received it, and was told by them that it had never been activated. They keep referring to it as my account, and I don't feel it is. Now they want me to sign a form stating that the charges made to "my account" were fraudulent. Do I have to sign this, when technically I don't feel it was my account.