Yes, you are correct. But, I'll have to tell you, I am around a large number of school teachers and other public school officials due to my work and my wife's association with a large group of friends who are all teachers. Based on my personal knowledge of these individuals and their political leanings (to a person) I stand by that generalization.
Let's put it this way... A local police officer was invited to the local school to speak with a few classes of elementary students. The teachers (three young twenty-somethings, fresh out of college, that I happen to know personally) refused to allow the officer to come into the classes unless he had secured his gun in the trunk of his patrol car. The officer informed them that wouldn't happen, bid them a good day and left. They later had a "police spokesperson" (sans sidearm) come in and talk to the kids.
Yeah, guilt by association? You bet!
Sounds like a pretty smart move by the teachers, considering all of the police gun "accidents" that have happened in classrooms.
Here's one example: