This appears to me to be a deliberate attempt to call Obama’s eligibility into question even if discovery were to show that either there was no legal marriage recorded in HI or the marriage was bigamous.
However, absent a legal marriage between Obama’s parents, Stanley Ann was a single US citizen mom and the 1948 BNA would not have made Obama a dual citizen. No foreign sovereign would have any claim over Obama, as the founders stated to be their concern at the time of the drafting the natural born citizen language.
It's not so much claims of foreign sovereigns that the founders were worried about, but actually loyalty to foreign nations and/or their sovereigns. Of course at the time the US was almost unique in not having a sovereign. Switzerland, IIRC, also did not have one at that time.