Supporting Maddyfish above:
From the KY Attorney General (p. 5):
We are aware that KRS 527.070(1), creating a criminal offense for unlawful possession of
certain weapons on school property, excludes "institutions of postsecondary or higher
education". The fact that the legislature has elected not to criminalize the carrying of those
weapons on the property of institutions of postsecondary or higher education, however, does not
preclude the governing boards of public institutions of higher education from otherwise
controlling the possession of deadly weapons on their properties.
This is an opinion reviewing the legality of the University of Louisville banning firearms from its campus. The Attorney General says that the university may do so -- however, as noted above, no legal penalty is connected with such an action.
You are confusing your reading of statues. KRS 527.070 which you make reference to is often misunderstood by our fine public servants. If you look closer at it, however, you will see that the prohibition of carrying on school grounds (whether public or private) does not apply to institutions of postsecondary or higher education -- see the first paragraph.