Could be ... but I don't believe the FEC's charter is to establish qualifications; they're just in business to ensure that the election machinery itself is operating according to law.
I believe that the matter of qualifications is left up to the States; and in that case, I would think that at least one of those offices would have positively established the qualifications of ALL candidates on their ballots.
Which raises the question: with all of the lawsuits and hoo-raw, has anybody bothered to ask their local SoS whether or not they've certified eligibility?
The FEC charter does NOT include verification of candidate eligibility!
What agency (or agencies/organizations) are charged with the duty of verifying candidate eligibility?