Obama could not be ELECTED to the office of the President. But he could be ELECTED as VP and he could be APPOINTED as either POTUS or VP. Nothing in the Constitution restricts him from being APPOINTED to either office and nothing restricts him from HOLDING either office. He is restricted by the 22nd Amendment from being ELECTED to POTUS but he is not restricted from being elected as VP. He could be elected as VP and then APPOINTED as POTUS and he could then HOLD the office of POTUS. (Birth Certificate issues aside.)

Obama could not be ELECTED to the office of the President. But he could be ELECTED as VP and he could be APPOINTED as either POTUS or VP.