The only thing a background check would do (have done) is (was) move the problem ........ not eliminate it.
Think it through.
The nut case would eventually end up in a tower somewhere (figuratively speaking) shooting innocents....at which point FP's whole "government pigs" argument goes out the window.....just as many dead, but not working in a shipyard.
There is NO way to stop people like this shooter. You can't block all the doors......he'll still get 'er done.