Y'know, it's one thing for Republicans to smear Obama as an out-of-touch elitist. It's quite another for them to use his attendance at Punahou as a data point in that. As the son of a Punahou alum and the grandson of a Punahou art teacher, I won't stand for it.
In all seriousness, Punahou is indeed an insanely rich institution, thanks in no small part to Steve Case's extensive donations. It is, indeed, pretty much synonymous with the Hawaii elite. But Obama is the antithesis of your typical Punahou student. He was on scholarship, as Jason Zengerle says, but more critically he was black in a school that's overwhelmingly Chinese and Japanese. There were more Haoles then than there are now, but black students are and were almost unheard of.
For his part, Obama has a sense of humor about the ridiculousness of the Hawaiian private school system. While my mom went to Punahou (where her godmother, Mabel Hefty, was Obama's favorite teacher), my dad went to Iolani, which is Punahou's less rich, dorkier, more math and science focused rival. I mentioned this to Obama at a Nashua Pride game last summer, to which he quipped, "So I guess you come from a mixed marriage too, huh?"