Given the fact that the US is a country of over 300 million people, and you have heard only a few stories of shootings, I find this comment extremely hyperbolic.
I went to private and public schools in 3 different states. The public schools I attended were extremely safe, but the private schools provided more structure and discipline (that someone like me was helped by when just a clueless kid).
EDIT: Also note that my best friend went to the well-accredited, local public school, and was valedictorian (eventually graduated from Emory Law). I went to a non-profit, private school where my roommate was on a full-ride, and went on to go full-ride to Carnegie Mellon. I blew off college and became a ski bumb/river-guide/waiter for six years.
My high school was fairly strict on rules and regulations, and my time and movement was managed and regimented to an extent that I've never experienced before or sense. Much of this was due to misguided safety rules. That was before Columbine, and from what I hear things have become far worse now.
Such might be reasonable if shootings were a serious threat, but the aren't, as you point out, so it's basically just wasted.
That's not a simple thought experiment, it's a massive data-collecting exercise.
I'm not sure if there are any countries with wholly-private education systems, are there? Still, there are many countries (the UK and Australia spring to mind) where private schools play a larger role than they do in the US. And your fears appear to be unfounded, as the private schools in these countries range from "truly excellent" to "quite reasonably okay". Parents and students choosing a school aren't nearly as misled by glossy brochures as you might think -- the newspapers are filled with detailed comparisons of average marks in statewide tests, success in getting into universities, and so forth.
Now I didn't go to a private school, I went to an academically selective public school in Australia, but there was always the sense that we were in competition with the private schools... their mere presence drives the public schools to try to do better as well. The main criticism that I could make of the private schools where I was (apart from snobbery and often-silly uniforms) is that they had a tendency to spoon-feed education to their students in the interests of maximizing their university entrance marks... the result being that students often floundered somewhat when they actually got to university and were expected to learn in a more self-directed way. But faced with a choice between that and a chaotic American public school where the primary goal appears to be stopping the students from shooting each other, I'll take the spoon feeding and straw hats any day.