I also believe that those borders are tightly monitored by the border patrol. If this person owns land on both sides I'm not sure how that is dealt with....Any land located in the wilds of Maine would not be an area I'd want to hike in. Pretty remote.
My grandmother came from Johnsville, NB and she used to talk about skating over the river to Maine or going over to Mars Hill - and there were no border crossings. I have been to Johnsville and I know first hand the border crossing is time consuming - especially into the US.
Also, the title of your query is ME (Maine) and the Canadian border. Vermont is not next to Maine - New Hampshire is.