My situation was rather specific. I hold several Security Clearances from different Government Agencies and the person who reviewed my case could see no reason for me to be denied at all which led to my second interview.
When I say appeal I mean write the Ombudsman and state exactly what you feel. That you have no knowledge as to how you don't fit the set characteristics of a Global Entry member, how you don't feel you did anything wrong during the interview process, but question the procedure that was followed during the interview detailing the oddity of the questioning of who you partner is and the follow-up call asking for his name for flagging.
If you can wait for your partner's interview to be completed also as that could give more weight to your reconsideration if he were to pass or fail.
Good luck.