Can a Werewolf actually hurt another Werewolf?

This came up today in Curse of Strahd. One of the werewolves wanted to aid the party in taking out some of her fellows.

It occurred to me that a Werewolf in hybrid form does piercing (bite) and slashing (claws) damage which werewolves are immune to.

Are werewolves actually immune to other werewolves assuming said werewolf does not have access to a silvered weapon?