Hi, I'm the guy who discovered the quirk in the first place. You can survive pretty much indefinitely at the river, with or without food. You could cross the river at any point. I just thought it would be a laugh to see if you could get to a five-digit year. Then, upon resumption of the journey, the party very rapidly deteriorates and you can only survive about 5 or 6 days before they're all dead, even if you gather food immediately and wait to restore health. So the unmodded achievement was "I lived for 15,000 years in The Oregon Trail" and then I asked moralrecordings for help in reverse-engineering the game so I could get the satisfaction of a successful arrival.
Just a bit of fun.
edit: And the answer to "Why THAT river?" is simply that it's the last river in the game, and when I was hoping to complete a run without any modding, I thought it might be possible to play normally, get to the final river, wait 15,000 years, and then try to limp my decrepit deathwagon to the finish line before we all expired. This proved impossible, sadly.