This article says,
Towers rose up, allowing eminent families to battle each other across the rooftops (most were knocked down by the authorities in an effort to prevent the perpetual state of neighbourhood warfare – although the Embriachi family’s tower was allowed to remain as a reward for their leading role in the Crusades).
Mostly, this makes me want to read this guy's book, but the particular image of medieval Italians brawling across rooftops, Assassin's-Creed-style, makes me want to know more about who these families were and what they were fighting over--and also whether that (admittedly ridiculous) idea is actually what was going down ^(or up?).
Yes! There is primary source evidence supporting Walton.
It's from Benjamin of Tudela, a twelfth-century Jewish traveler from Spain who recorded an impressive account of his travels across the medieval world. It's available online in translation from Project Gutenberg. The relevant passage:
From Marseilles one can take ship and in four days reach Genoa...Each householder has a tower to his house, and at times of strife they fight from the tops of the towers with each other. They have command of the sea. They build ships which they call galleys, and make predatory attacks upon Edom and Ishmael and the land of Greece as far as Sicily, and they bring back to Genoa spoils from all these places.
So: rooftop assassins AND pirates!
Some context: the various families were fighting over political control of the city, accusations of destroying each other's property to gain an economic edge, blaming each other for the accidental or intentional deaths of key family members--the usual. The clan wars eventually settled down around 1190 with the decision to start appointing an outside administrator, called a podesta, who would serve basically as a neutral figurehead ratifying decisions the families wanted while allowing them to not appear subordinate to each other.
Sources are Benjamin of Tudela's Travels, linked above, and Steven Epstein, Genoa and the Genoese, 958-1528 (2001).
hi! no mentions of rooftop battles here, but these posts will give you some leads on noble families and their defensive towers
What could be considered the very first "vertical city?" - featuring /u/AlviseFalier
Been watching too much Game of Thrones: How much time would an important medieval lord spend in the capital versus in his own lands? How did this change over time? - featuring /u/Enrico_Dandolo
The first post has been archived, so if you have follow-up questions, just ask them here & include the relevant user's username to notify them