He was ineligible this time based on the 14th amendment, but SCOTUS told Colorado they couldn't keep him off the ballot.
I think we can understand why SCOTUS would ban Colorado from making that decision themselves, for much the same reason it bans Mississippi from having its own interpretation of the parts of the 14th Amendment about due process or citizenship.
In contrast, the 22nd Amendment is plain-letter law, so obvious that it brooks no interpretation.
And as as far as the 12th Amendment goes, "But no person constitutionally ineligible to the office of President shall be eligible to that of Vice-President of the United States."
The 22nd amendment doesn't explicitly say he cannot serve as President, it just says "no person shall be _elected_ to the office of President".
Yes, the spirit of the constitution clearly prevents a 3rd term, but it could be possible to employ a very literal interpretation that allows the above.