Technically the Democrat party picked both of them. You are just plain wrong. Biden is still eligible, as far as we know, for the office of President. The Electors can and will probably vote for him for VP, although they could vote for him for President, and some other Constitutionally eligible person for VP.
But McCain might very well end up as President, if the rules were strictly followed and Obma was not found ineligible until after the electors vote.
I thought it goes to the House and Senate at this point, with the House choosing the Pres and the Senate the VP. In which case, we could have a Biden or Hillary Presidency and a Palin or Biden Vice Presidency.