It is possible that the BCs were prepared in batches. The information for 2-3 days of births might be given to a secretary to prepare for signatures. The secretary could have just taken them in the stack order rather than in birth order. (Unlike today, back in those days, the birth mother was kept in the hospital for a few days after the birth, so there would have been no big hurry to prepare the BC.) Given the time and the technology used at the time, I don't find this too alarming.
What I can't get my head around, is why would someone spend a reported $2 million to fight the release of a supposedly non-damaging document? Even if it is someone else's money, it makes no sense. If this is taxpayer money, then the taxpayers have a right to know why that money was spent.