Because William Shakespeare was a writer of fiction, rather than non-fiction (true history), any contention against him as a "fake" is completely unfounded.
While both The Merchant of Venice and Romeo and Juliet are set in Italy, they are mainly set in the fictional realm of high romance. In fact, the "wise man of the theater," Harley-Granville Barker, English dramatist, producer, and critic, declared The Merchant of Venice a fairy tale, reminding audiences that it cannot be interpreted in terms of realism. Indeed, the stories of the caskets, the pound of flesh, and the pretty young woman disguised as a lawyer are the stuff of fairy tales.
Similarly, Romeo and Juliet, with its "star-crossed lovers" whose violent and impetuous love of but a few days, is also a fairy tale. For, no realistic story could contain so much action and acts of fate--plagues, multiple incidental deaths, retributive acts, and parental dominance--in such a short time.
With respect to the Italian settings, these are not meant to be documentary; rather, they are created as a climate for the action and personalities of the characters. In Venice, the setting for The Merchant of Venice, verisimilitude is created with the Jewish merchant, Shylock, since there was historical antipathy on the part of the Venetian merchants for those Jewish merchants in this great trade center of the Renaissance. Likewise, Verona, an ancient city of Italy, represents a realistic setting for feuding families. In fact, what was purportedly Juliet’s house (Casa di Giulietta) is yet a significant attraction of Verona with the most famous balcony in the world.
.. in order to offer the countless couples who come to Verona every year a worthy location, the city of Verona bought today’s house of Juliet from the Dal Capello family in 1905. Due to the similarity of their names they declared the house to be the family residence of the Capuleti family.
As a dramatist, Shakespeare made use of the settings of Venice and Verona merely to generate verisimilitude for his plays, not to record any history.