Yes you can. Also, you can land on the same tile as another player only if it is a large tile.
Are you sure about that? In the rules it states that two people can only be on a large stone simultaneously, while the small and medium stones were restricted to one player only. I played the game at Gencon, so my attention to details may be sketchy, but I didn't see anything saying that the rules with the small and medium stones only applied when you ended your turn. Indeed, the guy giving the demonstration said you couldn't move through other players. Although, I'll be the first to admit that the demonstrators didn't seem terribly confident or competent about the rules.
Edit: A German guy in another thread said the German rules explicitly say that you CAN travel through other players. It seems Queen Games would make sure their demonstrators really know the rules before unleashing them on the public.