¿Puede mover sus dedos?

This is a phrase from the Travelogue course. Shouldn't this be:
- ¿Puede moverse los dedos?

I do see examples of this on the web but I thought that you don't refer to body parts in the possessive in Spanish: my teeth, my leg, ...
 

That is my understanding as well. In the weekly Spanish conversation group that I attend, that subject came up recently and the moderator (a former university Spanish professor) said that not using the possessive is correct but sometimes it is used in informal situations, or among less educated Spanish speakers.

I suspect if you or I used the possessive in this case we would sound like gringos.

I suspect also it's people who are perfectly bilingual that make these kinds of mistakes as well - mistakes that native monolingual people wouldn't make. It would behoove RL to have the latter check the courses before releasing them. This example is by no means an isolated case.
 

Steven, you're correct in that it's normal to not refer to them as possessions.  However, it's not a hard and fast rule.  One day in the local tienda a young boy was helping me.  Upon handing me a 7 liter jug of water, his fingers got pinched between mine and the handle, which triggered the response, "aahhh, mis dedos."
 

Thanks the-hefay. It's really helpful to hear examples of what is said down "en la calle".