The shooting in Little Rock is about to erupt into Spy vs Spy before the facts are in.
Quit thinking two-dimensions. Think in terms of dynamic statistical distributions. For any large polytropic sample, there will be edge cases in every dimension or trope. As the stress increases marginalizing some members of the population, they will exhibit ever more extreme behaviors in an attempt to reassert control. Both sides have been building with extremes, but it is the left that has the most diverse coalitions which are fragile.
That doesn't mean the left is the source. It means it is contributing the most stress to the overall polytrope.
McVey was far right. Oswald was far left. There is no reliable predictor of where it comes from just that it will come.