It is not about me, i am no the person who approved the CBRA and US passport and i think it is not that important to know which consulate. call 202 501 4444
The number 202-501-4444 is the same line as the toll-free number
1-888-407-4747 that I called earlier, see:
http://www.travel.state.gov/about/info/info_308.html#children
Just for the heck of it, I just called the 202-501-4444 number and talked to a customer service rep there (this time it was a guy). Again, I asked the question three times, just to make sure, and he said that, absolutely, at least one of the parents must be a U.S. citizen at the moment of the child's birth in order for a CBRA to be issued.
When I told him about your situation, he said that a CBRA should not have been issued in your case.
I still very much want to know which conslate you got a CBRA at. This is important for the other readers of this forum in order to understand if the information you are providing is correct or if what happened in your case was just a fluke. It is possible that the people working at that particular consulate are interpreting the law incorrectly.