First off we have a really snotty catalogue of little Charmaine's working class signifiers followed by: "a study confirms exactly what I have always believed. Academic success is infectious. Pupils 'catch' cleverness from their friends."
Unless that study covered the influence of pink leggings, electronic toys, pierced ears and soft play on intellectual development- then the study does not "confirm" her stupid prejudices.
Cleverness is not an exclusive middle class trait- IQ varies among individuals of all classes. Class privilege can effect attainment and life outcomes however, which is why I would assume that a study looking at the effect of friendships on achievement would control for class.
This alone should put Katie on guard against applying the findings rigidly to her own children's lives: as they very much do benefit form class privilege. This is a very important factor in predicting their course in life. Much more so than any effect of their choice of friendships I would expect.
She makes a couple of references to children's attainment coming from the attitudes and commitment of the parents, which is closer to the mark (and contradicts her own argument!). She wants to be cautious about assuming her own home is some kind of intellectual hothouse however, when its clear from her own writing that she is unable to formulate a logically consistent argument.
I have to agree with the person up thread who predicted lifelong problems forming friendships for her children.