IIRC, the buyer is not required to sign a bill of sale. If the document has the buyer identified, that is what is important.

Is it better to have the buyer sign a bill of sale, sure.

If the BOS says sold in "As-is" condition, tell him you bought it. Caveat emptor Proper due diligence on the buyers part is lacking if they complain now.

Honestly, this seems to be a common practice anymore, buy the car, it shows up and complain about what was purchased.