There's "controversy" because of the trauma to the collective national psyche. People want to believe that larger forces are at work, commensurate to the mythos of a national leader.

But if you just examine the facts of the case, it's obvious what happened — a tiny, pathetic little man assassinated a president — with a confidence approaching 100%. (But not getting to 100% — it's important to always maintain your scientific skepticism.) See for example _Case Closed_, Gerald Posner's nearly 30-year-old book. https://www.posner.com/case-closed