They weren't. The account had the SSN. The payment came under the other SSN. The filing was joint with both of our SSNs through the accountant. The agent I finally got on the phone after days confirmed that the problem was some mismatch between SSNs in the account, check, or filing.

Of course it was cleared up, but the point is that at least one of our SSNs was on everything. That should be a trivially easy for record merging or linking.