No all accidents are reported, then not all damages are accurately reported. So when you get a car fax, you are most likely getting only part of its history, and what you are getting isn't always accurate. Carfax even states that.
Like me for example, I've never claimed my fender benders, off roading, or engine problems. I just fixed everything myself and moved on. Plus I'd be more concerned about the mechanics of a car and not the cosmetics. Car fax doesn't really cover that if at all.