There are lots of stories about lots of things, many of them maliciously false, simply untrue, or incomplete. Rumor mills grind out strange stories because (1) the teller has only part of the facts, (2) the hearer only hears part of the facts, (3) and subsequent hearers trying to piece together the pieces jump to interesting conclusions as imagination fills in the holes. Of course the malicious facts are sometimes thrown into the mix in order to color events. Finally, memories can be really, really tricky things that cause pain to honest and well-intentioned people when recollections fail to fully match the facts that others present.
One of the facts is abundantly clear--FDR suffered from poor health for a long time. Churchill and Stalin both saw from their last meeting, where they planned their places the post-war world, that FDR was definitely not well (and Stalin took full advantage of it). Another fact is also abundantly clear, very sick people often die before well people. He had to go sometime, so while the papers and books often report "shock" at the news, it was a shock of disappointment to their hope that this honored and respected man would see yet another crisis his country was in, through to a successful end.
If someone said they heard someone say they saw him slumped over his desk with something in his hand, I can accept that. But what if it was his pipe or a stick or a long, narrow, open bottle, such as had his medicine--and someone commented from the glimpse that it looked like the barrel of a gun? We would do his memory great disservice over a snippet of interpretive thought which we have taken beyond its substance. Even today, it is no strange news for police to shoot someone in the shadows when it looks like they were pulling a weapon when it was only a cellphone, or an asthma inhaler. Honor your teacher for the teacher that he was, but place that story in a distinctly lower spot, okay?