If you can't see the distinction between easily verified proof of age vs assumed guilt for a criminal act that has never been tried or proven, I'd have to question your right to be anywhere near a legal proceeding.
We do need an
official and verifiable vetting process for candidates - to include clearly defined process and requirements. Age should be easily verifiable; we do a lot of this kind of thing to get a drivers license or passport; why should the process to apply for a passport be more rigorous than getting on a ballot, and why should it be more tedious to be permitted to buy a weapon than to get on a ballot? Legal disqualifications should be uncovered with adequate screening - which should be in place simply because many positions (legislature and president) involve access to classified information - candidates should be required to pass the same screening that military personnel do. Still every few years someone (usually in a local race) is accused and sometimes found not to actually reside within district bounds.
Whether right or wrong, this paper asks a lot of applicable questions and raises valid points.
Rethinking Presidential Eligibility