absolutely. i live with a harovian, and know 2 others, and a few etonians too. there isn't a bias. it comes down to the perceived quality of applicants.
my 2 cents, is that elitist parents who send their children to public school are all for equality as long as they can cheat their way into top universities, as soon as poor people start to achieve they are very quick to slam them down. consider grade inflation. now, you tell me, how you can put millions into education, improve teaching and opportunity, then complain when more people get As. it's a completely elitist attitude, and it stems from the arrogant belief of english public schoolers that on the basis of their privelege they deserve entry to a prestigious uni.
they don't interview (and i know because i only got in on special appeal) because it doesn't differentiate candidates very well. i didn't get in to edinburgh, and i'm never far from the top of the class, others who got in with ease struggle, there's very little correlation between quality of applicant and quality of student, which is exactly why they have BBB as they believe this is an adequate standard depending on circumstances.
I took "easy" subjects at a level - religion, english lit, music tech, and yet i outperform swathes of public school students who took hard subjects and got straight into edinburgh.
getting in to anywhere is a lottery, if you don't make the cut it's not a reflection on the quality of you, that's just the way it is!