It can be dangerous to look to Shakespeare for an accurate portrayal of history, even of historical eras and places that were fairly close to his own. He wasn't interested in portraying history accurately; he was interested in telling a great story. As far as we know, he learned everything that he knew about the societies that he wrote about from books, many of which we now know were full of inaccuracies. We don't have any evidence that he ever left England, let alone traveled to Italy, so everything that he knows about what Verona was like almost certainly came secondhand from books and stories that he may have heard from people who had been there. It's important to remember that Shakespeare didn't actually know if anything he learned about Italy was true, so it’s best to look at Shakespeare's plays as fictional and not to expect them to be an accurate reflection of history.