No the exact text is: "But no person constitutionally ineligible to the office of President shall be eligible to that of Vice-President of the United States."
The "But" changes the landscape - it means all before the "but" is true up until the conditions after the "but" are in effect.
If BJC is ineligible for president, he is ineligible for vice-president, after the "but".
I'm sorry, but I'm not following your reasoning at all. Like I said before, I do not think it is clear if Clinton could run as vice-president or not. Feel free to have the last word reasserting your rock-solid belief that he is ineligible.
I am not trying to have the last word.
The "but" is an instrument of language that seperates one set of conditions from another set of conditions in the discussion of a topic.
The sentence with the "but" is meant to sya, essentially: "Yes, satisfy the above you can be president, BUT if these other conditions exist, you cannot be president."
"...reasserting your rock-solid belief that he is ineligible."
Rock-solid? You bet. Doesn't mean someone or some entity won't try to "nuance" it to death.