I think it is ridiculous to make everyone who comes into a school have a background check. It is completely paranoid to go around thinking everyone might possibly harm your kid. I'm not suggesting we be lazy with our children, but there are few boogy men and we should (statistically) be looking within our own families/friends for anyone who would harm our kids.
And I am one of the unqualified teachers you are talking about. I have a degree, although it isn't in education. I think that although qualification has a place, there is too much emphasis on it. I think I'm a great teacher. I work hard educating my students. I have a great deal of experience teaching in different settings. However, if you were looking at qualifications only, you would miss out on all of the rich experience I have. Only looking at qualifications is a very narrow point of view.
As a side note: There is a great need for English teachers, which is why sometimes a warm, English speaking body is hired.