Insurers are an industry built on risk assessment. If two insurance-purchasing schools are exactly the same except that School X has Additional Circumstance Y, and Y makes the risk of injury or death more likely according to their evaluation of the data, then the insurance company is going to charge School X more money for insurance. If Circumstance Y makes injury or death less likely, then they'll charge School X less. (Presuming there's a reasonable amount of competition in the market.) Simple as that.
And what, pray tell, do these sober, green-eyeshaded heros of bean-counting say when forced to put their money where their mouth is concerning the arming of teachers?
If you do that, your insurance premiums are going up.
Note: and while the idea of having lethal weapons in arm's reach of six-year-olds wasn't enough to dissuade gun lovers from proposing more guns on campus as a solution to our guns-on-campus problem, school budgets are so tight (thanks, anti-tax crusaders!) that according to the article, the prospect of losing insurance or having to pay thousands more per year is making several of the quoted districts seriously reconsider the notion.