The point I was making is precisely that it is the cultural view point that matters not the precise citation thank you for reinforcing my point although you clearly did not mean too. One caveat though the Vatican did not believe in burning witches then or now whatever the public thought. Belief in the existence of witchcraft is heretical as it grants Satan real world power which is the purview of God alone
Slightly more complex than that. Before about 1200-1300, it was indeed true that the Vatican (and the Catholic Church more broadly) explicitly disbelieved in the very
existence of witches. That was in the Code of Canon Law about 1000 AD, and secular law reflected that (shortly after Hungary became Christian, laws against witchcraft were abolished "because there are no witches", for example).
BUT, and this is often overlooked, the belief in witchcraft came back with a vengeance by the Late Middle Ages, while Europe was still pretty uniformly Catholic. The 1300s saw a steady rise in the number of trials, and then the 1400s saw a more rapid rise--and then the publication of the Malleus Maleficarum. I'm not entirely sure
why the belief returned, but I think the overlap in time with the social trauma of the Black Death (~1350) is extremely suggestive--I think people were looking for a scapegoat. The prevalence of Dominicans in witch hunting also suggests that the Inquisition, invented to fight Catharism, might have settled on witches as a new threat (to justify its own continued existence). I've also heard it suggested that renewed interest in Roman and Greek literature might also, ironically, have played a role (since the existence of witches is taken for granted in many such works).
(sorry, just a nitpick of mine; Catholic apologists have largely memed the notion that witch trials were a Protestant invention into widespread acceptance, but that just oversimplifies the real history)