I'm with you on System 1, and that is a big flaw in the way Libet and Wegner present their results. But more importantly, on further thought, their causal diagrams are probabilistic. So possibly, you're right: our beliefs about lack of cause could be caused by an actual indeterminacy, while in an otherwise similar deterministic universe their beliefs are caused by something else. I was wrong to object to that claim.

I still see no appeal in such indeterminism, but that's another story.