The backup withholding will be shown on a 1099 at the end of the year.
You add this into the taxes paid and it increases the refund (or decreases the payment required).
If you don't support the W-9, they don't know you are not subject to the withholding. Withholding has nothing to do with tax liability. You get back what ever payments/withholding you have made that is in excess of your liability.