Regarding a preference to state school pupils with the same academic results over private/public school pupils I also think that is also ethical. A state school pupil will have had far less resources spent on them to reach the same academic results as a private/public school pupil and so it is likely that they will surpass private/public school pupil at university.
Well, the admissions departments (I worked in a school for a while, and although I wasn't technically a teacher I ended up being privy to a lot of exams/university issues from the kids) aren't supposed to just favour state over private, but they do make allowances for people whose education has clearly been substandard or interrupted. Some public schools aren't much, if at all, better than the local state school from a purely results-based outlook.