Yep........ but he didn’t fail to qualify did he under the existing rules/laws/statutes in force at the time of his filing. The states allowed him on the ballot, they didn’t get any proof that he qualified. The voters voted for him. The electoral college voted for him and Congress certified the election as valid. Never was he asked to provide the proof of his qualifications was he? Until that is put into either the US Constitution, Federal Law or State law we be electing Presidents that don’t have to show any proof.
I think that the twentieth amendment is "IN" the Constitution. We don't know the answer to whether or not his eligibility status was verified by Congress as per instructions to do so by section three of the twentieth amendment. That is why we have a problem.