I seem to recall five or so possibilities at the minimum. And they remain possibilities. They tend to provide much more plausible explanations as they do not require a person to invoke conspiracies.
So to answer your question, I think the folks you spoke with at HDOH are inaccurate when they try to describe how the process was done in 1961. A process of which they have no first hand knowledge. Nor even second hand knowledge. And in all likelihood was before they were even born.
Notice your epistemology.
You come across mutually exclusive claims.
So you write it off as just people pretending they know what they’re talking about when they don’t.
How would you falsify that belief? What would convince you that the numbers really don’t match up?
The archive of the article referenced isn’t available, but a small blurb about it at http://www.iolani.org/wn_alum_062708_cp5.htm says the June 2008 article notes Onaka’s 40+ year career in public health records. That tells me that he began his career before 1968. The HDOH Administrative Rules for the territory were converted to state rules in 1962 and no changes were made to those rules until 1972 when COHB’s were eliminated and 1976 when the current form of the rules was adopted.
IOW, Onaka - who told Okubo what to say about this issue - was in his public health records career when the procedures that applied to Obama’s BC were still in effect.
That calls your explanation into serious question.
What were the other explanations for the discrepancy?
I remember somebody saying maybe the numbers weren’t given sequentially. Maybe they hopped around with the numbers at the HDOH office. But in their 1961 Natality Report the CDC specifically said that the 50% sampling they used was reliable because the numbering at the state level WAS done sequentially. And Hawaii law has always required HI certificates to conform to the standards of the CDC (and its predecessor). Current CDC standards not only require that the numbers be given sequentially but that they begin with 1. We know the Nordyke certs are sequentially numbered.