I definitely think it's a generalisation, like so many other things about ASD.
DS1 (5.5) has a DX of ASD (aspergers type presentation according to the formal report, though admittedly at the milder end of the spectrum in terms of how his daily life is affected) and he most definitely both wants friends, has them and talks about them (I've also seen other children at school pointing DS1 out to their parents and saying things like 'look mummy, look, there's my friend DS1', so they're definitely not a figment of DS1's imagination, and his teachers describe him as having 'quite a wide social circle'). According to his teachers he is also able to participate in imaginary play as well as the boisterous running-around-the-playground stuff.
However, he definitely has issues with social communication, auditory processing and so on, and comes across as being immature for his age in terms of how he interacts with the others, but he kind of gets away with this as is one of the youngest in his class anyway. In reception he tended to 'fixate' on one particular child at a time and only want to play with that child (even though other children would try and initiate play with him) - this has broadened considerably in Y1.
DS1 is probably best described as socially a bit clumsy - keen to interact but not always sure how best to go about it, and this gap will probably widen as they get older - but he is generally keen to be around other children and most definitely doesn't prefer to play alone. That said though, he isn't crestfallen if for whatever reason there is no-one to play with at playtime - he just goes off and collects stones instead .