“Methinks someone faked BHOs document, and forgot to check for sequential integrity.”
We need to know the procedure the hospitals and registrar used back then. It might be that they only forwarded paperwork every few days from the hospital to generate the birth certificates. There’s a date of Aug 11, 1961 stamped at the bottom of both Nordyke’s as “Date Assigned by...”
Remember, 1961 was a lot slower than things are today, no computers or data systems to speak of, and paperwork was done by hand and moved at messenger speed at best.
The part I'd like to know is where the certificate numbers were/are added. It appears to be a Bates-stamped number affixed by the registrar. Most vital records offices I've seen have two or more deputy clerks sharing a single stamp while working on separate stacks of documents, so it is possible that the date / sequential number disagreement is simply the result of one worker being a bit faster than the other.
I've seen enough public records offices that used to divide up the work in that manner (particularly pre-computer) that I view the out-of-sequence numbers as literally "close enough for government work". It's not a smoking gun, by any means.