If she was really his teacher at Punahou, that part of the story is not second-hand.
I believe that he really was born in Hawaii on the stated date. But I know that older well-meaning people often confabulate - their memories fail and they add in additional "facts" to improve on their stories. So there has to be something else to back up her story about the birth before people rely on her word.
What causes you to “believe” he was born in HI? The COLB posted on websites, or his autobiographies/memoirs?