There is no conspiracy. There are one or two inconsistencies in people's stories, nothing more than that.
Another thing about conspiracy theorists: they ignore, as you call it, the blindingly obvious, then keep searching and manipulating facts, figures and dates until they come up with ever more bizarre ideas to support their theories.
As I read recently, if the US Government couldn't even cover up a bungled break-in to a crappy hotel in Washington in 1972 by a bunch of incompetents, then how on earth could/would they cover up things like JFK and 9/11?
It would be funny if it wasn't so pathetic.