We can certainly have a discussion, but it's outside the realm of logic, because there's no possible evidence that could disprove it. That doesn't make it true or false, but it does make it useless to discuss in the terms of logic, and trying will just lead to frustration.
What would we do differently if the shadowy elite was behind JFK's death? What would we do differently if the shadowy elite wasn't behind it? What ends were gotten by the shadowy elite through the means of mysterious assasinations to help the Rolling Stones sell records?
These are all reasonable questions to ask, but the philosophy of logic won't help us come to answers.