> Sure, but there's a huge difference between the targeted "hey I read your latest paper and I had a few questions about section 2.4" and "Dear Entire Physics Department: Einstein is Wrong! Here's my book". I honestly don't think I've ever received the former from a non-scientist (I'm not famous, so go figure) but we definitely got a lot of the later.
Well, I know quite some people who left academia because they became victims of academic politics, or just had enormous difficulties getting their employment contracts extended, despite doing great research. I get research papers from this kind of people somewhat regularly. All of them look at least very plausible to me.
When I was still in academia, I honestly only know these "crackpot stories" from narrations (dark fairy tales); I never got any "crackpot papers", even though the particular research area is said to be prone to crackpots (perhaps the reason was that crackpots need some basic knowledge about the respective research area to realize that the colleagues of the institute actually do research in an area that is very related to their crackpot papers, so they never sent their crackpot papers to my colleagues).