I believe this may be the case if Obama's mama claimed her baby was born "en route" ... according the standard procedures, children born in transit, such as on a ship or on a plane, can claim the arrival city as the place of birth, even though they weren't born in that city. Thus, it's possible that Honolulu was the city of birth but officially the child was NOT born on the island. Second, if the baby was born while crossing the international dateline, then maybe they can't verify which day he was actually born on. That would explain why Onaka didn't verify the date of birth.
Onaka verified that the info listed on the White House image is also listed on the record at the HDOH, so Aug 4, 1961 and Oahu are both on the record they have. So that can’t be the reason to not verify those “facts”.