I have rather extensive experience (25+ years) debating philosophical/theological issues with internet atheists. The "discussions" (to use the term loosely) go nowhere and quickly become tiresome. Your tactics are quite similar to those in the Internet Atheist Playbook.
That's actually a great analogy, because the tactics of the faithful are quite similar in both cases. They use all the same logical fallacies.
No, we cannot "prove" Oswald alone killed JFK or God exists as a matter of metaphysical ontology.
You can't even prove Oswald had anything to do with it. Just like you can't prove that a "god" directed evolution. The "Look at the trees" argument is similarly ridiculous to the "where are the curtain rods" argument.
I do not even insist Oswald would have been found guilty in a court of law; OJ wasn't, even though I would'ce cheerfully flipped the switch on the electric chair. We can only assess what seems to us the best evidence and most reasonable inferences in their totality and reach some level of conviction.
The problem is that everybody thinks his own "inferences" are reasonable. It's not at all objective.
On that basis, I have a strong conviction that Oswald was and did pretty much exactly what the Lone Nut community believes he was and did.
That's fine, and you're entitled to your opinion in both cases, but it shouldn't surprise you that non-believers are not convinced by "read the bible" or "read the Warren Commission Report".
My best assessment of the evidence and inferences is that no conspiracy occurred. Why this would bother you, I have no idea.
Why would you think that bothers me? People who believe that faith is a good way to determine what is actually true don't bother me, I just think that it's not.