Well they could go the alternate reality route, like each difference results in a new time line type deal. The paradox only exists if there is only one time line.
I know that some crazy physicists kinda disproved the multiple realities idea by questioning where the energy (and by that extent matter) would come from if we were creating reality after reality based on each change or decision, but they could just ignore that I guess. Or maybe they just ignore the whole thing and say look it's Bruce Friggin' Willis he eats paradoxes for breakfast! with a slice of toast.