I think you are right to some extent Greatnan, but I should declare an interest because our youngest DD was privately educated. Most of her school friends were from ordinary families, like ours. Their parents were plumbers, builders, teachers, small business owners etc. No really wealthy families, just parents who wanted a good education for their daughters and were happy to give up their luxuries for the duration.
We were driven towards private education by the experience of DS2 who had a difficult time at state school because he was interested and intelligent. He was bullied for asking/answering questions in class and certainly didn't reach his potential at school, though he has done very well since and now has 3 degrees and shown that he is a natural born academic.