In her case, it really was a combination of being overly sensitive to their behavior & a lack of common interest, but she did desire peers to connect with.
Yes. This echoes my experience with my DD, now 14. It wasn't that she wasn't interested in having friends, just that she wasn't interested in being SO radically not who she is in order to maintain the facade. She preferred, mostly, to keenly observe the behavior of peers instead of interacting directly. A sort of Jane Goodall of the elementary and middle school culture, if you will.
This sounds so much like my dd. That's why I get the feeling she really doesn't care if she has friends or not. There is a girl in our neighborhood who goes to our school and is in her class and I've offered so many times before school started to walk down with her so we could meet this girl and her mom and dd just plain doesn't want to.