My DW is working class and someone at her school told her she wasnt 'right sort of person' for Oxford so she did it all on her own anyway.
Luckily our tutor was a very open minded man and could see past her broad Geordie accent, wild hair, odd clothes and her 'not very good Comprehensive' and gave her a place.
I do think though having worked in and around the City and big business there is more than a modicum of truth in the article. Knowing how to behave in certain circumstances, how to eat properly, how to make conversation, how to use language properly all matter a lot in the higher levels of the professions and business life.
Broadening horizons and giving children sight of the possibilities and the basic tools of social interaction to make the most of their talent is surely worth doing.
My children go to private school and it gives me the rage that even there things like eating properly, behaving politely at table, eating together are not a part of the normal school day or even regarded as important.