A friend of mine has 3 boys, and they're all brats to the hilt because she doesn't bother disciplining them. One of them cracked me over the back with his "light saber" (a long cardboard tube painted green), and kept going - the mother did nothing. Finally, I reached around, grabbed him, laid him in my lap, looked in right in the face, and said, "We do NOT hit." Of course, he started screaming "Mommyyyyy...." My friend said, "She's not hurting you." I was FURIOUS.
First of all, I'd stop inviting them over. You can't control other kids, or the way the parents choose to (or not to) discipline them. If your friend asks what's going on, carefully and graciously explain to her that you've noticed her child has a hard time around the other kids, and until those issues get resolved, you'd rather not expose her to your children any more than you have to at this point.
If I were a betting person, I'd say that this poor child is acting out to get attention from her parents...negative attention is better than none. Whatever issues come out during the play dates is a result of a more serious problem inside the home.
In a way, you're husband is right. Typically they can work it out on their own. You know how? One of the kids finally "has had enough", hauls off and clocks the kid, which usually puts a stop to the bully's actions. Not sure I completely condone that, but I wouldn't stop it from happening either. It's one of those "Karma" things - what goes around comes around.
I remember when I was a kid, there was this boy at the pool who just kept bothering me. One day, he threw a tennis ball at me - hit me right in the chest. I had had enough - grabbed the ball, chased him around the pool, towards the tennis courts, out through the parking lot....never did catch him, but never had him do stuff like that to me again.
Keep a watchful eye and see what happens, but meanwhile, I'd proably stop asking your friend over until her kid starts behaving.