The phrasing of the poll question made it unclear whether the respondents know Hawaii was part of the U.S. in 1962.
Statehood is irrelevant to the question of citizenship. (Hawaii became a state in 1959.) The rule is you must be a “natural-born citizen” (or citizen at the time of the establishment of the U.S., but that’s not relevant anymore), not “born within the borders of a US state.” People born in territories, and Hawaii has been a territory since 1898, are natural-born citizens. Otherwise, Barry Goldwater, born in the Arizona Territory, would not have been eligible to run for president in 1964.
Coincidentally, John McCain, who not only ran against Obama but who also holds Goldwater’s old Senate seat, was also born in a US territory, the Panama Canal Zone. Although McCain also qualifies as a natural-born citizen because both his parents were US citizens.