Like Heather said, cultures are not conclusive. Depending on what part of the lung the culture comes from, bacteria can easily be missed.
I also wanted to add that pseudomonas cannot be obtained at school any easier than it can be obtained at the grocery store, or even in your own kitchen. It is impossible to avoid. The best defense is teaching excellent hygeine. You are going to hear scary stories of pseudomonas that shows up in showerheads, sinks, etc. He cannot live in a bubble, but you can do your best to keep his environment as clean as possible.