I agree that social skills can sometimes be the problem and not the cleverness, but sometimes there are no problems like that at all.
It could simply be that a child just doesn't have much in common with the children he or she is at primary school with. My ds does have some problems with social skills, but that was made worse at primary school because he genuinely didn't find anyone there that he had much in common with.
It was a lovely primary school, full of lovely children and lovey teachers, and ds was never bullied or made fun of at all as far as I am aware. He just simply didn't fit in, and didn't find anyone that he wanted to make the effort for. Trying to help him improve his social skills was very difficult when he wasn't interested in the things his classmates were interested in anyway.
Now he is at grammar school, there are lots of children that are interested in the same things he is interested in. He has things in common with people and wants to make the effort to get to know people just because they are more on his wavelength.
That is exactly what I wanted for him out of grammar school, it had very little to do with the academic achievement at the school, but I do think he is likely to achieve more there than he would at a comp because he will be happier. This is why it annoys me when people argue against grammar schools by saying that clever children will be fine wherever they go. They won't. School is about more than just the exam results at the end of it.