Yes, but it isn't necessary to recapitulate the 12th amendment.
I see your argument though, that "election" and "eligibility" can somehow be construed differently. The argument has to boil down to "Clinton is not constitutionally ineligible to the office of President," even in light of the 22nd amendment. I wouldn't want to be the one making the argument.
That's because you are not a leftist sociopath.