For what it's worth, I was just told on the phone by a supervisor at the official GOES support line that, for Global Entry at least, one doesn't have to disclose dual citizenship. (The issue in this case is our new (U.S.-born) baby, who by the laws of another country is technically a dual citizen, but has no documentation from that country that we could provide to prove it.) According to her, "lots of people who have dual citizenship just list their U.S. citizenship", and since GE is a program for admissibility to the U.S., this is fine.

Even so, the thought of not disclosing the other citizenship still makes me very, very nervous.