Funny you'd mention that.
Spoiler:
My only disappointment with 11.22.63 is that they went for the single shooter theory.
It's always disappointing when you come across something like this cause esp. in the context of fantasy you want to see a complicated conspiracy.
But the point of it all was mainly about time travel and that when you want to fix bad things, those very bad things actually lead to good things. And that by doing a good action, you may actually make things turn for the bad. You can't play with the laws of physics.
Anyway that was the point of the book I read(never watched the show).
The idea of the single shooter is somewhat redeemed where King gives a reason why this occured. Oswald in real life already tried to assassinate a retired General and missed so he had a few screw loses, that's proven. And after Oswald had decided that Kennedy was his enemy, not too long after he was hired in the building where the JFK car was supposed to drive right in front of. And when Oswald learned about this he felt he was invested in a destiny of sort. Like he had to do it, as if God was giving him a sign. That's pretty logical to me that somewhat like that would think like this. I thought that was clever writing by King.
Then again, the possibility remains that someone may have put him there.