Yeah, I’m not trying to push that particular schtick. I think my wife got a copy supposedly aimed at teen girls for my youngest, so there might be even younger versions. And we acknowledge that even the DC approach requires that you want to WFAIP which, in many cases, might require that you sublimate your personality and tolerate some things in others you might not really want to put up with.
But I know there are various “socialization” resources for younger kids. The parents might want to spend some time in the appropriate section of their bookstore/library (if they haven’t already). There will be stuff across the map - it may take some trial and error to come up with an approach that makes sense to your friends. And other than books, various organizations ranging from school to county social services agencies have activities, courses, lectures etc on socilaization, avoiding bullying, etc. But if they are really concerned with this situation, they may need to put some of their personal interests on the back burner for a little while, while they try to figure out what is going on and how best to address it.
Another approach is to keep exposing the kid to different activities, such as scouting, athletics, church, etc., hoping that eventually she’ll strike a chord with a kid she meets somewhere. But it is a bummer when your kid says she wants to hang out with a kid who lives 2 towns over, instead of on the next block.
If the one “friend” is a good kid and you get along with her parents, it can be possible to work with her parents to have the kids socialize more, and to have the “friend’s” parents discuss with her whether she treats her friends differently in school than on-on-one.
And as a parent it is very natural to keep saying to yourself, “Why does it have to be so much work just to raise a happy, social kid?” I’m not sure if we have blinders as to exactly what it was like when we were kids, or if our expectations are just higher nowadays.
Also - in grade school girls can be incredibly mind-bogglingly evil. It really REALLY sucks! I was astounded when somewhere around 2d grade my eldest was invited to be in a “club” that, as far as I could tell solely existed to exclude others. And dealing with the school or the parents of these evil-bitches-in-training can be an exercise in frustration. To some extent, you might be able to find other parents who feel their kids are being similarly exiled, but there is a real limit as to a parent’s ability to make friends for their kid - nor should the parent need/want to assume that role.
Finally, try to figure out what, if anything, the kid might be doing to exacerbate things. For example, on one occasion when one of my kids had few friends, we were mortified to learn that she pushed/hit one of the few kids who came over! Come on, kid - work with me here!
No easy solution - just the long-term heavy lifting involved in responsible parenting.