Interesting theory.
I don't think we've discovered enough about the laws of physics/math, or the world/space to determine what the full scope of science is and how our reality is made. I think our knowledge is so small that trying to claim we know the way the world is a reflection of our own hubris.
Computers can't generate random numbers yet, but computers were created by us and our idea of how everything should be working. Perhaps there are such things as truly random events in our physical world that we don't know how to replicate (yet).
If so:
When Bob pushed the button to go back in time, if a truly random event changed the course of his life, he might not find himself infront of that button, or might find himself making another decision with the button.
The question we'd need to ask ourselves is if the random event occurs within Bob that changes his trajectory, or if the truly random event is something that our world possesses. If within Bob, perhaps we have free will. If external, perhaps we don't, but something external to us does.
Deep thoughts, either way. Thanks for taking the time to write that.