Frank,
I agree that your advice is correct.
However you are allowed to offer a "same date of service, date of payment" fee reduction schedule. This is fine.
Since the other payers will not/do not ever pay on the same date of service, they do not benefit from the fee reduction. They are privvy to it however, and if they want to start paying me on the same date of service I will offer them the same discount.
I'm not worried though, the big insurers will never agree to it.