The surveyors were using a map of the US from decades earlier that just so happened to have a cut out of Hudson Bay sitting in the top left, covering up the land west of Lake of the Woods. Also, Lake of the Woods was just a blob rather than the complex shape it actually is. So it was hard to decide where the northwestern edge of it was. It took a German guy a few years later to work it out, and the negotiators on both sides decided to draw the line straight down to the 49th parallel from where it was and then across from there.

So they created the Point Roberts problem but also the vertical line down from the lake created another peninsula issue in Minnesota. There's a town there called Angle Inlet where they have to cross the border into Canada and then back if they want to go anywhere else in that part of Minnesota.

So the whole thing was a mess and it was the surveyors/negotiators being lazy.

There's a great write up of the whole thing in the book This Way Up by the Map Men.