This is fair, since Venice itself was a former province of the Byzantine Empire. The ruler of Venice was the Doge, which is Venetian dialect for Duces, a Greek title for Byzantine noblemen. The Aristocratic title 'Duke' in the west derives from the same source. Late in the first milennium the Byzantine province centering on Venice became increasingly independent from the Imperial capital, partially due to its support for Pepin and Charlemagne of the Franks, against the Lombard rulers of north Italy, recognized by Byzantium. The relationship with the Imperial capital waxed and waned over the next several centuries, with the vagaries of war and politics.
Even now there are churches of Orthodox architecture within this area of Italy and nearby Croatia. The great Saint Mark's Cathedral in Venice is an example, and still has icons of the Emperor Justinian and his Empress Theodora, which are great tourist attractions. Venice took control of the coastal area of Croatia, including the islands, nearly as far south as Greece. This is the source of the Roman Catholic influence in the Balkans, since Venice stayed with the Pope in Rome instead of the Ecumenical Patriarch at Byzantium after the Great Schism of 1054 AD.
In any case the Byzantine/Venetian/Italian connection maintained a close relationship of the West with the continued and weakend Roman Empire in its Byzantine capital well into the Renaissance period. As Byzantium fell into decay, and early modern Italy grew wealthy, Byzantine scholars and artists were hired to bringt the knowledge of the ancient world to Italy, and on to France and the Holy Roman Empire of the German Nation.
Sigh. Thank you for this lovely education of all. I often think how lovely the world would be should Byzantium have survived.