Not going to shoot holes in your theory. I LOVE theories. Here's the thing . . . your theory would suggest that the family started out for "the mountain" waaaay earlier than we had thought. Of course, this makes sense given the sheriff's comment about EARLY AFTERNOON or early evening!
I also firmly believe that something happened on Thursday, which was why we weren't TOLD about Thursday by the parents at first . . . we thought that they arrived on Friday. (For the same reason, I now believe that IR is KEY, which is why he wasn't mentioned at ALL in the parents' first "story" of their camping trip. He knows something, saw something, is not "with the plan". )
I'm not quite sure that it makes sense for them to have arrived at the campsite first and then gone back for "food" and left Jessica. Maybe! I mean, why not stop on the way? Surely they knew "gee, we're supposed to be on a few day camping trip, and we didn't bring anything to eat, no hotdogs, no chili in a can, not even fixins for s'mores!" I mean, they could hardly expect to survive on "the catch of the day". Anyway. I still think that whatever happened may fit in with a mom n' pop drinking at the bar and grill and leaving little Deorr in the car scenario. Not sure how the filthy fits in, how it happened, whether it was from getting out of the car when Mom and Dad were in the bar n' grill, and falling and hurting himself, or whether it was done by the parents to "cover up" bruising, but the filthy is somehow important.