It seems unlikely that you could, as oxbridge simply want the best students, regardless of their background. However, saying that, it would not surprise me if it was true and does happen sometimes, corruption is rife in all tenets of society, education and politics - so why would Oxford (specifically) be exempt from this? I'd go further to say that this probably happens in other top universities around the world, but far less often than might be thought.
We have to also look at this case specifically. This man is going to study law. The whole "we want the best students" thing is sort of meaningless in most art subjects. With the sciences, if you have the best students then you can carry out the best research, become more recognised and receive more money from private companies to further your research. This does not happen with say Law, English or History, to such an extent. Because of this the whole selective process and judgement of candidates or even the regard of graduates' work is far more murky.
So yes, I doubt that this happens often but I'm not foolish enough to believe that it never happens at all. Probably a few people every year might gain entry to such institutions due to their background or wealth, but I expect that this would almost always be in the Arts and is something that could never be fully eradicated.
Edit: What's up with the negs? I was merely stating in my post that some people can be bought. They exist everywhere, in every institution in the world and so to believe that Oxbridge is immune to any sort of corruption at any scale is completely delusive. It is possible that people in the past have got in due to money, power or other means. Rather than explicitly "buying" their way into Oxbridge, it is possible that interviewers or the people in the decision process (some of which may be bribed) have noted these things and it has altered their judgement of an applicant, gaining them entry. As I said, this stuff probably also happens in many other universities world wide, but it is probably only a very minute number of students that actually do this nowadays.