Couple of data points from a call today:

I tried to pay with a USB MC debit, registered, but got the 'exceeds w/d freq limit' message. The card was purchased at a Jewel (Chicago-area grocer) and I'd registered it in my name. FWIW, looks like it was a card from older stock, as there is an '02/13' date in small print along a back/side edge of the card.

The first CSR was quite friendly, obviously in the US (not sure where, didn't ask) and said that you definitely could pay with a debit card. Had to transfer me to a supervisor, who was also very friendly. Did ask to confirm my name and address on the debit card, but seemed to be just routine. After the error message, he said if I got this cleared up to just call back and they'd process it again, no problem.