National Collegiate Athletics Accountability Act or the NCAA Act This bill establishes requirements for institutions of higher education (IHEs) that have intercollegiate athletic programs and participate in nonprofit athletic associations. Specifically, the bill prohibits such IHEs from receiving federal financial aid if the IHEs are members of nonprofit athletic associations that do not require annual baseline concussion testing prior to student athletes' participation in contact sports; require certain due process procedures for students and institutions prior to enforcing a remedy for infractions; require athletically related student aid to be guaranteed for the duration of the student's attendance, up to five years, and irrevocable for reasons related to athletic skill or injury; and restrict the ability of IHEs to pay stipends to student athletes. The legislation also establishes the Presidential Commission on Intercollegiate Athletics to review, analyze, and report to the President and Congress on certain issues related to intercollegiate athletics, including the interaction of athletics and academics, the financing of intercollegiate athletics, the recruitment and retention of student athletes, oversight and governance practices, health and safety protections for student athletes, and due process and equal enforcement of student athlete rules and regulations.