I suspect the Oxford\Cambridge undergrad interviews have less to do with assessing technical competency and more to do with providing admissions with a reason to discriminate against state-educated kids. The amount of Oxbridge intake come from private schools is disproportionately high to be due to exam results alone, and is better explained by an ingrained negative view of those with a state education or old boys networks.
I've seen this in action, exceptional state school students turned down from Oxford, and utter buffoons (but with the correct background and accent) being accepted.
There's no statistical evidence showing this is the case. Students from high performing schools are disproportionately likely to apply to Oxbridge, but adjusting for academic performance there's no indication that Oxbridge discriminates.
Pretty much everyone applying to Oxbridge is applying with top grades, plenty of exceptional candidates from both state and private sector schools get rejected.
While I suspect a lot of this probably does have to do with selecting "people like us" I've also had the experience to compare my privately educated son with my own experiences in state education (at a pretty rough school).
What private schools seem particularly good at is instilling a rather outgoing self-confidence that seems pretty uncommon amongst state educated kids. Note that this is effectively orthogonal to actual capabilities - but the end result is that I suspect that a lot of privately educated kids will come across a lot better in these situations than people from state schools.
It's not fair - but to be honest that's why you pay the considerable amounts of money for private education - to give your kids an advantage.
Assume for a moment that the exam results of students follow a bell shaped curve and that the mean and standard deviation of exam results in the state and private sector are the same, then you would expect the proportion of state school pupils accepted by Oxbridge to be the same as the proportion in the general school system. If instead we assume that the mean in the private sector is higher then you would no longer expect the same proportion to be accepted, and indeed that disproportionately many private sector students would get in.
I'm not saying this is the case (although private school students probably do do better in exams on average), but without knowing anything about the situation how can you accuse them of discrimination? The 'oh, I saw a really good person get turned away' argument is silly. Some colleges only offer a few places for some subjects but are presented with 20+ students who all have predicted straight As, good UCAS forms etc. It's inevitable that some good students will not get in, and it doesn't imply discrimination.
I have first hand experience of the Cambridge interview process and was successful despite being a state school candidate.
I read mathematics and my interviews were purely technical. (None of those "hundred uses of a toothbrush" for me - perhaps those were for the arts students ;-) )
In the UK we are in the unfortunate situation whereby school examinations are so easy (as a result of political intervention) that it is effectively impossible to distinguish between the best candidate on examination results alone.
Privately educated students do make up a much larger proportion of the student body than they "should", compared to the overall population. However, it could be (correctly) argued that state school pupils are more reluctant to apply in the first place.
I can confirm that at Cambridge between'97 and '00 there was a concerted effort by the university and the student body to encourage applications from statistically underrepresented sections of society.
All Harvard kids are rich rowers, all Oxbridge students are posh sons and daughters of politicians and aristocrats, and all these state-educated kids were rejected simply because they didn't wear the right clothes, amirite?
Bla.
I do around 50-60 admissions interviews a year, and we don't even know to which schools the applicants went when we question them. What you've seen in action is a few anecdotes and whiny parents who blame external factors for their child's rejection letter.
NB, I'm not saying there isn't a problem. There's still a lot of room for improvement; both universities are doing plenty of outreach work and are fully aware of the situation. But your portrayal of Oxbridge is ridiculous.
That's likely to depend hugely on the subject. I'm privately educated in relevant subjects, and went on to do an engineering degree at a well-regarded university (not Oxbridge, but ranked with them), but there's just no way I had the technical chops at the time to get past these questions. I don't think I'd even read GEB yet.
With a technical subject, it's relatively straightforward to put a meritocratic admissions system in place. I don't think you can make that argument for humanities subjects.
I've seen this in action, exceptional state school students turned down from Oxford, and utter buffoons (but with the correct background and accent) being accepted.