Unfortunately, I think the conclusions of the study are true, ie it is not just what you do as a parent that matters but who you are.
People generally (there are exceptions) want to stay in thier comfort zone. If your parents and all the adults you know are educated professionals who speak well and know the ways of "polite society" then that is your comfort zone and subconciously you will try to stay within it as you grow up. If on the other hand, the only middle class people you meet are your GP and your teachers and they are considered "not like us", it must be very hard to even think about aspiring to such careers.
A little anecdote... Recently I went on an evening out with friends and we were chatting about our children. My friend said that she took her 4 year old son to the GP and while the doctor was typing the prescription her son commented "Oh, you have a print of "Lilies" by Monet on your wall". The doctor looked surprised and said "How do you know that?" and her son replied "Because it is my favourite picture in the National Gallery". Now, the National Gallery is free to enter so in theory any London child has the opportunity to go, but I am sure it will not surprise you to learn my friend is a surgeon and her husband is an architect.