My guess is she entered through Bellingham but knowing how lax the border was in the 60’s I doubt the birth was registered at the port of entry. I don’t really know but I do know that the port of entry would NOT keep the original Birth Certificate! They would have given her immigration paperwork to fill out and have stamped, but would have returned the birth certificate to her.
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.
So you think they flew into Vancouver and then drove or took a bus to Bellingham on to Seattle?