You’d think people defining borders would take better heed of “measure twice, cut once”.
Except that you are thinking in modern terms, having very precise geographical data at your disposal. Agreements made in these historical cases HAD to be made with no accurate data available. Surveys would reveal that the terms of the border agreement created an anomaly. Given the data available at the time, it was reasonable for somebody to suggest that the US/British border extend west from the northernmost point of Lake of the Woods to the Mississippi River. It wasn’t until somebody adequately surveyed the region that they realized that the Mississippi’s origin was south of there, and early maps showing the river extending much further north were in error. Politically, there needed to be a border treaty between the US and England, unexplored territory or not.
Any chance of Point Roberts or Northwest Angle being turned over to Canada, eh?
I would say it was not reasonable to base a boundary on assumptions of undetermined geographical features. If they didn’t know the relationship of the features, the defined boundaries should have taken the uncertainties into account. For example, the border agreement should have had a clause for contingency that the river did not go where they assumed.
I’m not thinking in terms modern geographical data. Making mistakes because of imprecise surveying is understandable. Making mistakes because they made bad assumptions was completely avoidable. I probably should have said “measure before you cut” instead. 
You can’t get out of Carter Lake, Iowa, without going through Nebraska. Unless you have a raft. So does Iowa count?
Now, Toledo is sort of a DMZ, who’s status depends on who won the most recent Ohio State/Michigan game.