Greg's observation that Avery didn't appreciate his foster parents is clearly true. But given Avery's history, that is not surprising. I think Bill is right to be worried, but I also think he and Greg and Clay are really powerless to have any influence over the way Avery feels about Lee. They can try to keep them safe, but that can only go so far...
The nightmare that Lee had was a reflection of the nightmare he has been living and hopefully he is beginning to realize that fact.