“becomes at the time of his birth a citizen of the United States.”
He can be a member of Congress. A president needs to be a natural born citizen. Rubio does not qualify.
Your opinion, which the courts do not appear to agree with. In multiple cases on citizenship, the courts hold that birth on US soil, with the exceptions of children born to foreign diplomats and occupying forces, are citizens at birth. US Courts have recognized two types of citizens: born, and naturalized. (Some gray areas for those born abroad when only one parent is a citizen, resulting in legislated residency requirements as in Rogers vs. Bellei.)