I understand that Cambridge and Oxford usually know what they're doing when they offer places and there will always tend to be a couple of people who miss the grades, and the offers they make allow for that.
At my Cambridge college, for Law in my year (matriculated 1998), they made I think 12 offers and 9 people got the grades. The 3 who did not get the AAA didn't get in. There was one guy with AAB that they really liked, but they couldn't make an exception for him without it being unfair, was the view.
The following year, they made about 10 offers and only 1 person got the grades! So rather than having 1 student in the year, they let everyone in, believe it or not, so there was for example one student with AAC and one with AAE...