If he was actually born in Hawaii.
Did you know states can issue birth certificates to children brought into the country without actually being born in that state? Normally that isn’t important, but in this case it is.
Actually it is the other way around. He could have gotten a Certificate of Live Birth (COLB) from HI after the fact, and that is the (allegedly forged) document that was briefly posted on his site. He would only get a Birth Certificate if he was born in the state.