Yes, the notice states, "If they agree, send the B notice." The accounts did agree. The question was still, should I contact that contractor? The letter stated explicitly that I do not need to contact the IRS or prepare a corrected 1099. This implies to me that they already know he gave them the wrong number. Whether he was cheating on his taxes or not remains unknown. It was a substantial payment. They have his name and address, of course.
I did not send the B notice because there will never be any future contact with him and cannot be backup withholding.