The Guardian speaks in riddles. Its account of its origins are utterly self-contradictory. The Guardian says [
http://www.chakoteya.net/StarTrek/28.htm], "I answer as simply as your level of understanding makes possible." It's explicitly stated that what it says has been dumbed down. It's explicit that everything the Guardian says is to be filtered through that caveat.
In fairness, that's why I made the qualification of literally interpreting "All is as it was before." Maybe we're not supposed to interpret it literally.
But we do know the reason for the traffic accident, as it occurred in the events we saw. It was caused by the interactions of Kirk, Spock, and McCoy with Edith, and Kirk and Spock's deliberate refusal to save her. As indicated in the OP, if there was an original unaltered timeline, there would have to be another reason for her crossing the road that isn't in evidence. Spock's theory that "time is fluid, like a river, with currents, eddies, backwash" could mean that another reason would occur for Edith to get involved in a traffic accident.
But by the same token, Kirk and crew were drawn to the planet. It's like they were caught in a current that carried them there. Was it just to have an arbitrary, random adventure? Or was it because their actions were essential to the structure of the timeline, and it was literally necessary for them to be at that planet right then in order for existence to have the shape it was meant to?
YMMV.