Correct, one needn’t be a natural born citizen to be Senator, or Governor.
In a related matter there is the question of dual-citizenship. The years he is reported to have traveled to Pakistan, he could not have done it as a U.S. citizen because the State Dept was not allowing that. Thus, it would be interesting to see the stamps in his passport to see which country he was claiming to be a citizen of during that time. It wasn’t the U.S., I can guarantee you that. Dual citizens cannot be POTUS.