Wish I had a buck for every time I've read that from people who are spending tens of thousands on lawyers because "we trusted." More often than not, it's family.
No. It doesn't make any sense at all. Any sale or conveyance of property can have a title search as well as a title insurance policy. And anybody can sue anybody whether it's about a quitclaim deed or a warranty deed.
In fact, I recommend that B and C get an owner's title policy for their own future protection.