Hahahaha, what utter ********. I'm actually at Fitz and there is a substantial proportion of students from private schools and a fair few from public schools (I know people from Radley, Charterhouse etc here). That had absolutely nothing to do with your chances of success.
It doesn't have huge state sector intake anyway, it's much less than the national representation of state sector pupils and is more representative of applicants to the college, rather than any bias on behalf of admissions tutors (who, frankly, couldn't give a **** where you went to school).
Scapegoat your private school status all you want, but that had nothing to do with it, it probably had much more to do with the fact that your ability levels weren't up to scratch and you were intellectually inflexible - as they said in the feedback.