However, those along any border do not use that border without understanding a government controls its own borders. It’s understood by use of the word invasion, naturalization, defend, etc in the constitution and by the congressional power to pass any legislation that enables any of the expressly stated powers.
I would be looking for the best deal and the best idea if I were a landowner alongside a national border.
The property ends at the waters edge, the border goes down the middle of the river with the exception of a few small places. Plus the river has the ability to change course and has many times in the past, especially down in the valley where there are many old oxbows present.