I don't think "shiny private school children" is very rude...? Or was the rest of what she was saying unacceptable...?
I would never send my DS to private school and people who criticise private schools are not necessarily jealous; they may be left-wing, or have had a bad experience of private schools, they may want their kids to mix with a richer variety of people, be better prepared for the real world, or just think private education's pretty pointless.
As an example, I went to the state school in a small town where there was one (very good) state school and one private school. The state school had excellent ofsteds, outstanding GCSE pass rates, and regularly sent 10-20 kids a year to Oxbridge. It also had a private chapel, a purpose-built debating theatre, and extensive grounds.
The private school had a raging drugs problem, very mediocre teaching, and not one person I knew who went there went on to get a degree. Some dropped out during A-levels, several went to uni but didn't complete the course. Yet half a dozen kids I was at primary school with were sent to the private school, often requiring great sacrifices from their parents. I just didn't get it then, and I don't get it now.
But [hypocritical emoticon] I would move to a better catchment area, however I criticise myself and others for this, and recognise it is basically immoral.