Article II, Section 1 of the U.S. Constitution outlines the only prerequisites for one to be President of the republic: “No Person except a natural born Citizen, or a Citizen of the United States, at the time of the Adoption of this Constitution, shall be eligible to the Office of President; neither shall any Person be eligible to that Office who shall not have attained to the Age of thirty five Years, and been fourteen Years a Resident within the United States.”
Why wouldn’t one have to prove that he/she meets these requirements in order to get on the ballot? It just seems natural that, in filing the paperwork, one should have to submit, as a matter of uncontroversial course, documents proving eligibility under each criterion.