My point was broad. The administrator signs, but I am sure they do it only after consulting the coach. So, ultimately it is the coach who makes the decision. And the way that form is written it seems there is a lot of leeway for coaches to define terms.
Now talk about your bureaucracy, NCAA Bylaw 14.02.12 says:
14.02.12 Grade-Point Average. For purposes of calculating a grade-point average for NCAA eligibility (e.g., progress toward degree), a student must achieve a minimum grade-point average based on a maximum of 4.000 grading scale, unless otherwise specified in the legislation. (Adopted: 4/29/04)