The scrollbar inside the scroll pane will respond to styling changes made to the parent.
Will give the scrollbar the little blue highlights instead of the default haloGreen. But if you need to do other things, like in my case having a narrower scrollbar, then it gets tricky. I used the approach described here:
I've got a long history with Flash and it took me about 4 hours to fix the things that bugged me about the scrollbar and to make it narrower. I'm much happier with the scrollbar now. Of course I might well have stuffed up something and not even realized it yet, but so far so good.