I heard my version from Harry Fritz who taught the Montana history class at the U of M for years, (although his version made it seem like that the name was the only issue). He was also sure to point out that Missoula avoided a fate worse than death by being rescued from Idaho (although I suppose it still would have been “Montana”).
I think many Montanans so desperately want especially the drunken variation of the surveying party story to be true.
The version I heard just said “mistaken”, with no blame on drunkenness or anything else. Also according to that version, the straight vertical line part of the border was where a river crossed their path, and they therefore realized they weren’t on the divide any more, and so just said “screw it”.
I’m pretty sure I read that version in a Bill Bryson book (probably “The Lost Continent”). I like Bryson’s writing, but I wouldn’t trust him with any vital facts.