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There have been many attempts made over the years to clarify this such that it only applied to the actual property OWNED by the school while the school-sponsored event was ongoing, however none of these bills have passed and we are stuck with the legal language we have now:

Sec. 46.03. PLACES WEAPONS PROHIBITED.

(a) A person commits an offense if the person intentionally, knowingly, or recklessly possesses or goes with a firearm, location-restricted knife, club, or prohibited weapon listed in Section 46.05(a):
(1) on the physical premises of a school or educational institution, any grounds or building on which an activity sponsored by a school or educational institution is being conducted, or a passenger transportation vehicle of a school or educational institution, whether the school or educational institution is public or private, unless:

(A) pursuant to written regulations or written authorization of the institution; or

(B) the person possesses or goes with a concealed handgun that the person is licensed to carry under Subchapter H, Chapter 411, Government Code, and no other weapon to which this section applies, on the premises of an institution of higher education or private or independent institution of higher education, on any grounds or building on which an activity sponsored by the institution is being conducted, or in a passenger transportation vehicle of the institution;