Might they have made a photocopy of it, or even just a record of having seen it, along with some information from it? Or would the paperwork itself have the information on the place of birth of the baby?
Remember BHO Jr, would not be coming in as a US Citizen, so the BC would not be one from a US Embassy or Consulate, but rather a British Colonial one. Under the appropriate assumptions of course.
They might have made some type of copy and included info from the b.c. in the immigration paperwork.