Or, you could carry your passport any time you are junketing within 50 miles of the border, as a precaution against an inadvertent bump up against it.
Having never crossed the U.S. border in a private vehicle I don't know whether that precaution would also forestall a vehicle inspection.
I don't carry my passport unless I have intention of using it. The more you have it with you the more exposure there is to it being lost/stolen/damaged, etc.. It is a valuable document to me and I see no reason to carry it around when I have no plans to be needing it.
One of the nice things about the Canada/US relationship is the ease with which we can cross the border for the most part. I think that people who you don't live near this border don't realize how many border crossings there actually is and how many are on tiny little country roads in the middle of no where. It is easy to simply be out out for a mindless drive on a nice day in territory that you are not intimately familiar with and when just ambling down some nice country road you suddenly find yourself at a border crossing. There are even towns that straddle the border so there is no actual border crossing because it would be in the middle of a residential street in the middle of the town. You actually have to be careful of what direction you go in when driving down the street because you could suddenly find that you crossed the border and then you get escorted to the official border crossing by the border patrol. As I wrote earlier turning around in front of the border and taking off can raise suspicions. It has happened to me a couple of times. The problem with this is that you suddenly become subject to inspection which is fine but it is a PITA and time consuming when you are only going to turn around and head straight back in to Canada.
I know that there are many ways to avoid unintentionally crossing the border and it really isn't a huge concern of mine. I am not suggesting that it is an insurmountable problem by any means. The point I was getting at is that I can set the GPS to avoid gravel roads, highways, U-turns, tolls, low overpasses, narrow streets, etc, etc.. I would think that an international border is at least as significant as any of those items. Since the GPS is already programmed to know exactly where the border is I don't think that it would be a big deal to include it as one of the items that can be selected to avoid.