If a student athlete is injured during a game should this be recorded as workmen's comp?
By definition, a student of any particular institution is not an employee of that institution.
Whereas a student may be employed by the school they attend, their duties as employee constitute those things for which they are somehow compensated by their employer; and, those requirements they must meet regarding their status as a student are non-compensated, tending only toward their coursework. The two stations are neither interchangeable nor synonymous.
That which applies to the protection of a student while on school property is different from that which covers the school's employees; and, anything not done by one of the institution's employees during the regular course of their job which culminated in a mishap would not be covered by workmen's compensation insurance. This means that all athletes, if they wish to be covered by workmen's compensation insurance, need to get a job--- playing ball at school won't qualify.