I've had Billi do that for treats that were too big, too hard... Even stuff that I've seen her break up, sometime's she won't take it unless I break it. I figure she does have a tiny little jaw and chews a lot so she probably gets sore. I don't mind the extra effort. Heck, maybe they just want extra fuss out of us.
If Teddy's doing it only sometime's, I'd say his jaws a little sore, maybe...