While there will obviously be many exceptions, as a former teacher I can see an element of truth in the idea that summer-born children are at a slight disadvantage. There is nothing intrinsically different about summer-born children, but I think the approach of individual schools and teachers can affect outcomes later on. Many schools now monitor children with birthdays from April onwards for potential underachievement. A year's difference in age is hugely significant for younger children, and in the classes I have taught it has tended to be the older children who come up as as the 'high achievers' early on, often purely because they are more confident and mature. Sadly, from the Foundation Stage Profile onwards, children are often linked to a number/level, and when I was teaching Year 1, it was often the autumn-born children who came into my class with Reception scores of 8 and 9 in the various areas of learning. These children were then projected to be the academic successes at KS1 and KS2, while the younger children lagged behind, simply because they had less life experience. It's also the biggest, strongest (and therefore often oldest) children who make it into the school teams at this level - and who then get themselves a reputation for being 'sporty'.
I have a summer birthday myself (July) and while I was an academic high achiever and now have a Masters degree, at primary school I was consistently placed in a mixed-age class with the other July/August born children from my year and the older children from the year below. Although my teachers did try to differentiate the work by age as well as ability, this wasn't always effective and for practicality's sake, we sometimes covered topics from the academic year below, rather than what the 'older' class were learning. Summer-born children also seemed to be something of a rarity at my academic grammar school, as the vast majority of the other birthdays in my year group clustered around September/October/November. So there does seem to be something in this research.