Then you'd better read the Constitution.
The XXII Amendment creates a bar to election. It does not add "Ineligibilities" to Article II.
The ineligibilities are:
Under age 35
Not a natural-born US citizen (unless already a citizen in 1791)
Not resident in the United States for fourteen years prior to election.
No person who is Constitutionally ineligible to the office of President may be elected Vice-President.
Bill Clinton is NOT "Constitutionally ineligible".
He just can't be elected to the office of President.