You're right, but only about schools you personally know about.
Kwillia hit the nail on the head -- you have to look at the schools in your area and decide on that. Fact is, some public schools are great, and some suck. AND, just the same, some private schools are great, and some suck. You can't generalize all schools, public and private, based on just the few you know about.
It's all about the kid too, and whether or not there are special things they may need for school and if the school can handle it. My friend's boy is dyslexic. His public elementary school did wonderful with him in special classes to help him deal with it. So, she had no need to pay for private school. However, she was worried about middle school because her older daughter had grade problems in Leonardtown Middle. Well, she sent her son there to see how he would do, and it turns out he's doing great. They do great helping him with his condition as well. Seems her daughter was just being lazy.