LA Fitness Personal Fitness - Forged Signature Chicago, Illinois

A day after my daughter and I joined LA Fitness (my membership was required because she was too young to join on her own) we met with a personal trainer who tried to sign up for a year of personal training.  We were reluctant to commit, and he suggested we try it out for a month and then decide. We agreed to that, namely, to pay $160 for 6 sessions and then decide whether to continue.

As it turned out, they processed this agreement as if a commitment to 12 months, including $50 enrollment fee.  There started an endless sequence of phone calls to both LA Fitness and the credit card company.  Whenever I disputed a charge, LA Fitness provided the credit card company with the contract "I signed," only the "signature" there is not remotely like mine. Eventually LA Fitness waived the rest of the contract, but only from the period they deemed it appropriate, claiming I have to pay for personal trainer sessions in the period the contract was disputed.  The credit card company (AmEx) claim they cannot verify signatures (?!?).  I have both copies of my original, regular membership, contract with LA Fitness and with the fraudulent personal training one.  The two signatures are not remotely similar. 

At this point, AmEx claims I owe the disputed amount ($480, for 3 months), LA Fitness claim I should thank them for allowing me to terminate the contract (?) without penalty.  I checked and cannot file a report with the police on fraud since I don't know the identity of the person who signed "for me" and I cannot file a report against a corporation.   Thus, AmEx insist I pay and sort it out with LA Fitness, who insist that they already went beyond the call of duty by releasing me of an obligation that they unilaterally created.