J.D. Hayworth addressed that question on his show this week. Apparently, congress-critters don't have to show a valid birth certificate to get a passport.
I don't have any reason to doubt that, and assuming it's true, it's because being a citizen is a requirement for holding a national office.
But being a citizen is not enough of a qualification to assume the office of president of the United States. The constitution imposes a requirement that the office-holder be a natural born citizen.