The Vatican DID NOT EXTERMINATE the Templars. They were arrested and tortured by the French at the orders of the French king. Those Templars who lived outside of France were largely untouched.
This why Templars survived as an order even somewhat after the dissolution at Vienne. Read: http://www.brill.nl/default.aspx?partid=10&mcid=3&pid=29039
Who was a Papal lackey much the same as Hezbollah is an Iranian lackey
Oh come on !!! The Vatican could have stepped in but decided not to. They wanted the Templars gone as well.