Global Entry is meant for frequent travelers, and many of us frequent travelers do have 2 passports.

But regardless, the last time I went to the CBP office I only ask them to rescan my primary passport, but that didn't solve my problem either.

I asked to try my passport after they rescan it, but the officer claim that the only way to check is to go thru the real machine, which is within the arrival hall. (in LAX, the CBP office is at the departure hall, unsecured area)