Have you got it now?
Even better, I'll read it to you. Here's the important part: "But no person constitutionally eligible to the office of President shall be eligible to that of Vice-President of the United States". It doesn't help your argument.
There's a difference between being eligible to BECOME President and being eligible to RUN FOR President. The 22nd Amendment makes Clinton ineligible to RUN FOR President ("No person shall be elected to the office of the President more than twice . . .".) Unless he loses his citizenship, though, he still meets the Constitutional requirements to BECOME President (Art. II, Sec. 1: "No person except a natural born Citizen, or a Citizen of the United States, at the time of the adoption of this Constitution, shall be eligible to the Office of President; neither shall any Person be eligible to that Office who shall not have attained to the Age of thirty five Years, and been fourteen Years a Resident within the United States.") Because he's still Constitutionally eligible to BECOME President, he's still Constitutionally eligible to RUN FOR Vice President.