Final answer:
There is no evidence in the provided extracts that directly answer whether Alexander started a rumor about Giovanni's impotence, and without specific sources, we cannot definitively answer the question as true or false.
Step-by-step explanation:
The question suggests an inquiry concerning historical rumors and the reputations of historical figures, which seems to mix various historical contexts. There is no evidence provided in the given extracts to directly answer whether Alexander started a rumor that Giovanni was impotent. Given historical documents like those from Aulus Gellius, we know that rumors and personal attacks were not uncommon in Ancient Rome. Additionally, stories of Alexander from Abonoteichos, a religious figure who was also a known manipulator, suggest that creating and spreading rumors was a tactic used by some to maintain influence. However, without a specific source linking the Alexander mentioned in the question to any rumor about Giovanni's impotence, it is not possible to give a true or false answer to this question.