You found the Federal GFSZ law. Essentially nothing to do with BATF.
It means what it says - if you have a license from the same state as the school zone in question, you are exempt from the restriction. Without a license, must transport handguns and long guns unloaded locked in a case or a gun rack.
The Federal law does not account for places where a license is not required for some form of carry.
And GFSZ does not apply on private property that happen to be in that 1000' school zone.
California has its own version of GFSZ; I happen to live inside a GFSZ.