It's part of the same recording Berg tried to use (by taking bits out of context) to claim he was born in Kenya. Just listen to all of it, and it becomes crystal clear she knows he was born in Hawaii. I linked to a page that has a link to it above.
Advertiser columnist and former Star-Bulletin managing editor Dave Shapiro was not at either paper in 1961, but he remembers how the birth notices process worked years later when both papers were jointly operated by the Hawaii Newspaper Agency which no longer exists.
"Those were listings that came over from the state Department of Health," he said. "They would send the same thing to both papers."
And a phone call to the newspaper agency from a proud grandma would have sufficed too. Are they going to say no to a little blurb - I doubt it.