All these variances of the story are called rabbit trails/red herring. Look at all the coincidences and then say that you believe in the lone gunman theory. The umbrella was an umbrella, which in and of itself is highly suspicious, and I've never met any serious assassination researcher that believes this man was shooting poison darts. This is how it works: someone comes out with an outlandish, impossible theory (the poison dart, the driver did it, they were shooting from the gutter, etc.), they get all over the mainstream media and all researchers are tarred with the same brush.
If someone's theory cannot be refuted, then they are ignored, misrepresented and/or attacked in the media on a personal level, i.e., according to Posner and Bugliosi, 3/4 of the citizens of Dallas must be both drunk and insane publicity seekers. If you are as yet undecided on JFK assassination, I would recommend you look for the points that the various theories have in common. Think about how outlandish and improbable the Lone Nut THEORY is.
1) Did Oswald screw up the autopsy of the president?
2) Did Oswald cause forty different doctors and nurses at Parkland to describe wounds entirely inconsistent with the official autopsy?
3) Did Oswald appoint the Warren Commission?
4) Did Oswald harass/buy off/kill off the witnesses? Did Oswald alter the Zapruder film?
5) Did Oswald damage all of the existing assassination films at the exact same spot?
6) Did Oswald confiscate all of the other films that were never returned? In the Z film you can plainly see two men on the south side of Elm who appear to be filming the assassination at point blank range at the exact instant of the head shot...did Oswald steal their films? What happened to them?
7) Did Oswald sequester the evidence for 75 years? Why would National Security concerns require them to withhold the tax returns of a minimum wage lone nut malcontent? The truth is somewhere in there.
The media learned a lesson in 1963, so much so that they barely even questioned the official party line when MLK and RFK were assassinated, and by 9/ll they just read the script they were given like they couldn't see in their own video that there was neither a plane or any human remains in Shanksville. ....wake up...