In reply to Babika:
Some thoughts from someone who's done this before (and spoken to admissions tutors about the process)...
Cambridge interviews have a fierce reputation but are really just a 'check', the decision having been made (mostly!!!) before the candidate walks in. If the student has the right marks, good references, an interesting personal statement, then the interview will only confirm what the tutors think, check s/he is not bluffing, etc. Any surprises, positive or negative, will of course affect the outcome and the tutor's interest is always getting the "best" student, "best" in this case referring to the student that the interviewer believes will do best at the university. Different colleges and subjects (and interviewers) will have different interview strategies but the thinking behind the process will be fundamentally similar.
The point you make about changing questions as you get to an answer is completely standard, the line of questioning will start very basic—I had the unnervingly simple "So what sort of things do you like to read in English?" to kick off a modern languages interview—and become harder until the candidate reaches his/her natural limit, then the whole thing will start again up a different road. The process is opaque but actually quite fair, since it is verging on impossible to prepare specifically for these interviews age 18. Interviewers have a lot of contextual data available and will be able to tell a lot about background and attitude from a seemingly anonymous application system, much like recruiters learn to make inferences from CVs. There is no bias towards public/private schools in the admissions system, apart from the fact that candidates from those schools are perhaps more likely to apply to Oxbridge because they are inherently more comfortable with the traditions, etc. and the universities' status as "institutions" (but I personally would dispute this).
Regarding the attitude of the interviewer: it may be that the interviewer is a bit of a "scientist" when it comes to social interaction, it may be interview number X of the day/week/month, the decision may have been 90% made one way or another, who knows, who cares... all the other applicants in that subject/college would have had exactly a similar experience so the idea that it will disadvantage your son doesn't hold much water. Rejecting the university's offer of a place due to one antisocial tutor is another overreaction given that the university that your son/his mate would go to instead would have a more impersonal, anonymous teaching system than just an awkward tutor or two....
Post edited at 13:33