Joseph, what about people who send their kids to Orthodox schools who are dishonest in business, say lashon hara (I even know someone who imitates the accents of gedolei Tora and another who tells insulting jokes about various communities because they thinks it is funny), use bad language, etc.? The Gra says (Even Sheleima 2) that if someone has naturally bad middot learning Tora will actually make him worse. This is why Tora is compared to water. It makes everything grow. As for children who go to public school, would you differentiate between playing in your home and in theirs as perhaps the other kids will be influenced? What would you tell someone who has close non-frum relatives?
MW13, the mishna in Avot refers to an individual and his individual status. It does not make blanket assumptions.