That's an interesting allegation. Do you have any evidence that it is true? Unfortunately, the author of this piece fails to provide any.
It sounds like he's projecting current conditions back onto the past without really looking at the details.
I don't have any information either, but Hawaiian requirements for birth records were lax even when the welfare state wasn't much to speak of and immigration was limited.
Just why that was -- an effort to get around restrictions on Chinese or Japanese immigration and citizenship or just general inefficiency -- I don't know.
How likely is it that the White Territorial governments would have made things easy for Japanese newcomers? Maybe there were just too many children born on out of the way plantations to keep good records.