In the year 940, the Burgundian King of Italy, Hugh of Arles, was in a precarious situation. In order to consolidate his control over the Kingdom, he gave very powerful positions to his relatives, the Bosonids, in place of local Italian nobility. However, this did not sit well, and soon enough, he was lying in company with wolves.
That fateful year, the Margrave of Ivrea inspired the nobles to rise up against Hugh. Hugh was forewarned by his son Lothair II, and Berengar was sentenced to imprisonment. In a Machiavellian twist, Lothair II also informed Berengar of his arrest, and Berengar fled north of the Alps to the court of future Holy Roman Emperor Otto the Great, of Germany. Otto gave him protection, until 845 when Berengar returned to Italy and deposed Hugh, installing Lothair II as a puppet king, himself being the real power behind the throne.
However, what if Otto, not trusting his intentions, refused asylum and escorted Berengar back to Italy? He is imprisoned, rather ironically, first in Como, than in La Garda Castle, Canossa. Hugh is eventually deposed, by an Italian noble named Oberto. The Bosonid family is forced by the Italian people to flee back to Burgundy, where they would continue to claim the Italian throne. Lothair II and Adelaide live long, happy lives, free of the influence of Berengar. Because he does not come into power, presumably due to poisoning Lothair, he does not force Adelaide to marry his son, Adalbert. Adelaide, therefore, does not refuse and is not imprisoned, not treated badly by Berengar and his wife, Willa. That means that she doesn't flee to Canossa, where she would send a messenger to Otto the Great, proposing marriage and, essentially, 'keys to the kingdom.' In short, it is Italy, not Germany, that inherits the legacy of Rome.