Disagree. I have seen Catholic schools change lives of inner city youth because of faith formation and genuine care given to students of rough backgrounds
I also want to point out the increase of prevalence of mass shootings in upper middle class suburban school neighborhoods, the heroin/opiate epidemic in the northeast. Not to mention the antidepressant pharmaceutical culture invading the lives of the well-to-do, and the hyper extreme hazing of ivy league frat life.
All this to say: the formation of character is forged by a variety of complex factors.
It's kind of like what we always say about Muslims. You have a tiny percentage of them in a Western culture, they behave themselves. You get a few more, they start throwing their weight around. You get a few more, they start taking over.