I have to say this doesn't surprise me, it's a long time ago since I applied to Cambridge, but there was very much an attitude in a lot of state schools (mine included) of not encouraging certain pupils to aim too high; the head girl whose parents were both GPs was actively encouraged to apply, whereas because my parents had no formal qualifications and worked in low paid jobs, it was suggested I bear in mind that there were other unis, not put all my focus on Cambridge etc.
It's important to remember that there can be real divisions in state schools, the attitude at mine to those who had 'professional' parents and those who didn't was markedly different. It wouldn't surprise me that this sort of thing still exists, and might well come across at presentations etc - the only people I knew locally who had gone to Oxbridge before me were pretty much all horse riding, lacrosse playing v v middle class children, which I wasn't at all.
Indeed whilst most of my friends at Cambridge were state school educated, the majority were the children of doctors, teachers etc - being at Cambridge and growing up in a council house in Essex (as I did) was, in my massively upper class and right wing college pretty unique.
If I had my time again, and could choose any college, coming from the background I did, I'd pick Robinson.