If a appointment was scheduled, no paperwork was filled out, patient has never seen doctor before, and there was no reminder call. How can it be legal to charge a no show fee, if you were never made aware of one?
If you have health insurance you might consider disputing the claim for payment form the doctor's office.
I agree that in order for the office to have a valid claim, you should be on notice of the policy. If the appointment was made over the phone it is likely you can dispute any charges with the office, or come to a settlement on a lower fee.