And even with this power there are quite a few stories of people given sanctuary in monasteries which the civil authorities nonetheless seized. For the one that came first to my mind, visit Chapter 11 (The Slow Poisoners) of Extraordinary Popular Delusions and the Madness of Crowds and search for the word "Barri". Then read the tale of La Tophania. (OK that is not truly Medieval. But even then sanctuary was often more theoretical than real.)

An additional note. That is a book that is mentioned quite often, and despite having been in print for upwards of 150 years still sells. However virtually all mentions you will encounter only talk about the first three chapters...