In fact I believe the FAA is the only authority that doesn't bill foreign airframers for their services...
The FAA doesnt charge per se, as manufacturers self certify. The FAA authorizes a certification process. The FAA then approves the results of the cert process. ( that was a big issue with the 787) The FAA does have the 'undue burden' clause, which allows them to charge if the fees become too extensive.
While the FAA doesnt charge a fee for cert, they are paid an hourly rate for time and travel to review the results of the cert process. The manufacturer has to pay for the techincal expertise that the FAA requires for cert review. So while not paying the FAA directly, they are paying the expert. It is cheap to say the least.