Privately trained security is always a good idea. Most private companies have access to training well beyond the common LEO, in most cases. Are we talking about mall type security, Loomis, or the average sit at the desk and watch a monitor type? No. If we have trusted private contracted security to guard our Embassies abroad, on top of our diplomats, why would we not do the same for our country.
Security in schools should have been addressed many moons ago. After the Oklahoma City bombing, guess what happened? Security barriers, blast proofing Federal buildings (windows and structures in general), higher security monitoring and the whole 9 yards. Why? We wanted to protect those inside a possible target. It's sick that someone would even visualize a school as a target, but it's a big one. From random crazies, to the most brazen of terrorists, the children of this country are vulnerable targets. Where are kids usually found in mass quantities? Schools.
Proactive security is a great start. Actively engaging a potential threat would significantly reduce the chance of human loss or casualty. Does that mean shoot first and ask later? Hell no. Experienced personnel would only help promote a safer environment, not take away.