Right! So I had this very very frustrating bug as well, but I somehow managed to solve it.

First, I loaded a save from where I got all the witches head but hadn't turned them in yet. Then I simply refused to enter Jorvaskrr (?) and made sure that any potential quests in the Driftshade Refuge where next quest takes place were completed and done. After this, I simply roamed around doing quests, killing dragons etc. but still refused to enter Jorvaskrr. Last night, I decided to give it a go again - and received the quest to my great surprise (as before this Nothing worked).

So, my only 'solution' is: Make sure you don't have any quests at Driftshade Refuge and roam around and check from time to time. Do not attempt to hand in the quest without saving first. I'm not sure this solves it for those that's already tried to hand it in, but it helps to fix it if you notice that the hand in bugs it.

I realise this isn't the best solution, and that there's an uncertainty to it working - but at least it gives a bit of hope and I know that if someone had found something like this when I got bugged.

Good luck!

Confirming this.
To elaborate: Purity of Revenge apparently bugs out if the three final bandits in Driftshade Refuge are dead prior to handing in the previous quest in the series (Blood's Honor). Now, I believe it's been confirmed that "cleared" dungeons take 30 in-game days to repopulate, so if you wait 30 days before going to Jorrvaskr with the witches' heads, the bandits in Driftshade will respawn and the quest will trigger as intended. Note that you can enter Whiterun at any time during the wait, just avoid entering Jorrvaskr and subsequent completion of Blood's Honor.
This is excellent news for those of us who don't want to use console for any stupid reason (like me, I'm roleplaying, what the hell is a "console"? ) and the xbox360/ps3 players. You can just force-wait 30 days or spend it with some meaning to it doing other quests. Tada!
DISCLAIMER: I haven't tested how Helm of Winterhold quest affects this. For me, it has already been completed before I embarked on the quest to kill the witches (and I believe the helm was placed in a different location, I just cleared Driftshade Refuge while exploring).

I found an easier work around for this:

*I had the Helm of Winterhold Quest for Driftshade Refuge but I hadn't completed it before I started Blood's Honor.
*Fortunately I saved as I arrived back in Whiterun after completing Bloods Honor and before walking into Jorvaskrr so when Purity of Revenge didn't start I didn't lose any of my efforts
*I loaded the save mentioned above and went to Driftshade to complete the Helm of Winterhold quest, I cleared everything except for the 3 Silver hand guys in the last room. I just snuck over to the chest with the helm in it and then left.
*After turning in the quest in Winterhold I went back to Whiterun and spoke with Vilkas in Jorvaskurr and he joined me and started the quest and when I went back to Driftshade all I had to do was walk in and kill the 3 guys in the main room and collect the fragments. Everything completed properly and I have started the next quest after the funeral.
*I did not need to wait 30 game days for the dungeon to reset or anything like that