Yes, I think that those in the times had more knowledge of the situations during those times than we do. We attempted to interpret what Shakespeare was speaking on, but everything is just an opinion. Just as if some our stories and movies were to view by some of that time, they would have to guess about what was actually being said.
I agree that people in Shakespeare's time understood him better than we understand him today. All we have today is his works and history about him. We can grasp and try to understand him as well as possible, but only to the extent of what we know about him and the time period that the people lived in. We don't know a lot about him or the era becasue he is dead.