Having their cake and eating it too

That is the attempt of groups like Sinclair Community College. Their ability to have officers unilaterally arrest people is largely conditoned on their being a public entity. However, this Ohio organization has its officers declare an attempt at "private property" to arrest people for proselytizing.
Any public school is public property, and people have rights and can clearly NOT be arrested for tresspassing there.
Here is a link to the story http://www.onenewsnow.com/Legal/Default.aspx?id=539812