About the being born in a country: sorry, but that is total bs. Even leaving out special cases of children born on vacations abroad and the like (and only in some of those country you get that citizenship then, like in France or the US...not in Germany though, in case anyone was wondering. Which would also mean that children born in the US to foreign parents that spend most of their subsequent life somewhere else would be able to run for president.
I know a girl from uni who is German, has German parents, but was born in the US because her dad was working there at the time. When she was 2, they moved back to Germany. As far as I know, she hasn't been to the States ever since, but she does still hold American citizenship. Should she be allowed to run for president?
But again, away from that special case.
My entire family was born in countries that do not even exist anymore (Sowjet Union and the GDR, in case anyone was wondering)...would that take away all possibility for any of us ever to become president, anywhere?
In my opinion, citizenship is what should count. In case of dual citizenship, place of residence (in the past and present) could be the deciding point. When you choose to be part of a country, to (in some cases...like for Germany/Russia, dual citizenship is officially not possible and only granted in rare cases) leave your old country behind and from thereone live under the flag of that new nation, why shouldn't you be granted all the rights natives have as well? Isn't that actually discrimination based on origin? I don't know about to the US, but in Germany that's illegal!
There's a reason why citizenships aren't too easy to obtain. Correct me if I'm wrong, but in order to become an American citizen, you must've lived there for at least 5 years, 2 if you're married to an American, right? Shouldn't that be enough to become fully integrated into the country? On top, there's citizenship tests one has to pass, so only people who comprehend American laws, politics and culture are actually granted citizenship. American citizen should be American citizen. No matter if by birth or naturalization. (-> which is why I'm not a fan of those citizenships just thrown to anyone born in the country, but with to other affiliations).
Also, it's not as if just anyone can become president. I'm not entirely sure how the American system works, but I do know that there are elections enough. If people thought someone wasn't American enough to be president, I'm sure they wouldn't let him get that far anyway.
That said, I don't think Schwarzenegger should be president, ever, but not because he wasn't born in America.