We don't want to discuss the Connecticut tragedy directly, as the facts aren't all in, and politicizing it wouldn't be in good taste.
However, the broader issue the OP raised is relevant. There's some confusion on this. As enacted, the GFSZA states:
(A) It shall be unlawful for any individual knowingly to possess a firearm that has moved in or that otherwise affects interstate or foreign commerce at a place that the individual knows, or has reasonable cause to believe, is a school zone.
(B) Subparagraph (A) does not apply to the possession of a firearm—
(i) on private property not part of school grounds;
(ii) if the individual possessing the firearm is licensed to do so by the State in which the school zone is located or a political subdivision of the State, and the law of the State or political subdivision requires that, before an individual obtains such a license, the law enforcement authorities of the State or political subdivision verify that the individual is qualified under law to receive the license;
Many states have laws that are stricter, but Texas does not.