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Besides the Commune of Rome there were many other occasions when popes had serious troubles with the Roman nobility and Roman people, who weren't always willing to obey the popes. The medieval politics in Rome were so complex with political plots and riots that it would offer a fine setting for a strategy or roleplaying game.
 
I'd say yes even without checking that link,since the papacy and the HRE are the fakers tbh.

The conflict wasn't about someone being a faker. It was about who holds the secular power in Rome. Rebels declared themselves as the Roman Senate and while they denied temporal (but not spiritual) power of the Pope they recognised the (Holy) Roman emperor.

You have to remember that these people had very different ideological and historical perspective and often what seems fake to us was very real to them. In this case everyone who was involved considered themselves as the rightful successors of the Ancient Rome.