Right, but I'm thinking of a scenario where he goes off-trail or in the wrong direction at some point on the 16th.We know this from the timeline:
9/14: Dropped off by-boat at Terrace Point, Lake Yellowstone, by Trekking Adventure (3rd party, not the standard NPS Backcountry Boat shuttle)
9/16: Encountered a Ranger at the Howell Fork Patrol cabin, and the statement was made by NPS that this was "Not on his planned route"
9/17: 19:00+ at Eagle Peak Summit: Makes some cell phone calls, one to his Mom, and leaves one person a VM. Reports bad weather at Summit.
9/20: Fails to show-up for boat pick-up (again via Trekking Adventures, is reported missing)
Based on some of the details it's very likely that AK's backcountry permit either changed or was not updated from his initial plan: to start from outside the park via the Eagle Creek Trailhead (Eagle Creek campground). There was confusion around his Truck not being at the Trailhead, so this really points to the Backcountry Permit not being correct vs his actual route. Since AK was able to secure the boat shuttle through Trekking Adventure, he started on 9/14 at Terrace Point shuttle drop-off on south Yellowstone Lake. We do not know the specifics of the backcountry permit nor reservations for other backcountry sites on the entry/exit.
For example, say he takes the spur to see the Howell Fork cabin, but when he returns to the Mountain Creek Trail he turns the wrong way and walks south instead of north. Maybe that's unlikely as he should have realized that he was descending in elevation rather than climbing, but i just can't figure out why it would take him until 7:30 pm on the 17th to get to the summit of Eagle Peak.