You would get association rather than causality with the undergraduate-level media study, sure. You can impute causality with a statistical model, but a proper dataset on the myocarditis as linked to deaths simply doesn't exist here. To produce a quality study, a consistent autopsy process would have been required at the time, and that wasn't happening due to factors such as overwork and governmental disinterest in discovering the truth.
If you're saying that you insist on the standard of proof being published research, you're ignoring a whole bunch of stuff. Whatever was published yesterday is probably wrong, in the sense that someone else likely will show us what that piece of research missed later. You're also ignoring how politics at the funding level controls which studies you have the opportunity to read, and which ones you don't.
If we simply took the politics out of funding, and pursued the truth, the right would have a lot less ammunition for its conspiracy theories. Unfortunately, people are people and there's a large number of reasons why that's not happening, unless we turn the funding decisions over to a third party like computers or aliens.