The article says 'monopolised by', not reserved for. Which doesn't mean that the universities will pick a person from a private school over one from a state school, just that more of the places are occupied by students from private schools (which from my experience isn't the case anyway).
Kids at private schools find it easier to get places at Oxbridge for a number of reasons. One of these is simply that they are more likely to be encouraged to apply by their families and teachers. A higher number of applicants means that you are bound to get more offers (its statistics - think about it). Once you are in the system, the university doesn't care what school you went to, just how well they think you'll do when you arrive. Of course, you might be better prepared for the interview process if you've been at a private school, but there's not much the universities can do about that.
I'm not saying that its right that things are disproportionate - but remember, you can't jump to conclusions without actually thinking things through (which, I hate to say it, is what your reaction appears to have been).