How old is the child next door? My son is almost 4, very shy, and he doesn't have many friends at all. We go to a playgroup, but he still just kind of plays with ME only. Some kids aren't socially as "developed" at a certain age as others, and if this little boy is an only child, vs. your children who each have a couple siblings, that explains a HUGE difference right there.
Do you know of any playgroups or community-offered things for kids in your area? Maybe you could tell the mom about them and help her out a bit, or introduce her to some of your friends with kids. Maybe she just doesn't get out a lot and doesn't know a lot of people with children.