The context in which the study was done is clearly important. In Brazil, there was and is no clear divide in class/education/socio-economic/age terms between mothers who bf and those who don't, or who do for a short time only. This is obviously very different from the UK.
It is possible - as the researchers said - that the difference in outcomes in Brazil related to feeding are reflective of different sorts of mothering rather than different feeding. That is, mothers who breastfeed longer are somehow 'different', and it's the difference in mothering that makes the difference in intelligence/material success in life.
The study was revealing in that it appears breastfeeding has a 'dose' effect - the more it's done, the greater the impact - so it's indeed possible that Brazilian mothers who like breastfeeding and do it for longer are also more likely to do other things we know support cognition and intelligence such as having more frequent interactions with their babies, or being more responsive to their needs. We just don't know. However, knowing, as we do, that the very composition of breastmilk supports neural development (ie the growth and complexity of the brain and its function) in a way that formula milk cannot, the findings are certainly supportive of breastfeeding causing the results they found, at least partially.
But it's more complicated than that. It may well be that good, responsive and sensitive, loving care reducesor even wipes out the difference made by breastfeeding. It may be that being born in materially well-off circumstances with good access to education and higher education makes any feeding difference disappear, too. In any case, research like this does not and does not claim to predict outcomes in individual babies, which is why anecdotes of intelligent successful ff babies are irrelevant. It's on a population level that any difference emerges.
What makes me irritated is the way the research - in fact, any research like this - is regarded as a criticism of women who don't breastfeed. This is understandable when people feel defensive and sad about their breastfeeding experiences, but really....why don't we grow up a bit and see the wider picture?
What about the majority of mothers in the world whose circumstances are not materially good (including some mothers in the UK)? What about families whose access to education is poor? Isn't it good, that babies born in difficult circumstances can have something instant, cheap and readily-available that does make a difference? And that the health services and maternity professionals in countries with limited education and welfare provision can support women breastfeeding, knowing it does appear to help?
Breastfeeding is often precarious in the developing world - the idea of all women breastfeeding happily and exclusively for years is false. It could be that raising the overall IQ level and material well-being of a population by 4 points is a small step towards reducing inequalities, and one which should be supported alongside advances in education and other forms of welfare.
It would be good if in the UK everyone got a basic education in understanding research, so fewer of us left school capable of coming out with some of the odd, self-centred and naive notions expressed on this thread :(