Although I seem to remember hearing that the marker is actually misplaced and not at the intersection at all (inexpert application of a theodolite, maybe?)
The question of the exact location of state borders is actually a pretty interesting one. They were traditionally defined by lines of latitude and longitude (four corners being the classic example) but it's my understanding (and I'm not a lawyer) that the legal border is wherever the traditional markers have been placed.
This actually matters a lot for the casinos on the southeast shore of Lake Tahoe.
When you give geographic coordinates, to be precise you also have to give the map datum (coordinate system) in which they're defined. There are actually many, as prior to the GPS age every country had their own, and they were sometimes revised. GPS forced the issue; it's global (that's what the G means) so naturally it (or more accurately the US DoD, which runs GPS) had to define its
own datum as a compromise to all the others. That's WGS-84, the World Geodetic Survey, 1984 version, last updated in 2010 I think. Before that there was WGS-72, and a bunch of others. GPS receivers can usually be set to a number of datums, but nearly all default to WGS-84. So when someone gives you coordinates that's almost certainly what they refer to. And they're often quite different from the "traditional" coordinates used in many areas.
Because of the worldwide popularity of GPS, WGS-84 has become the defacto standard in most other countries so their users have to be very careful when using local maps drawn in a different datum. For example, if you've ever visited the Royal Greenwich Observatory in England, you'll discover that the
true (i.e., WGS-84) prime meridian isn't on any of the lines on the observatory wall that the tourists pose next to for pictures. It actually runs through the park a hundred meters or so to the east of the building. When I was last there I lined up some garbage cans on it so I could get my own,
proper souvenir photo.
The other datum that Americans are likely to run into is NAD-27 (North American Datum 1927) which is what all those nice USGS topographic maps are drawn in. NAD-27 and WGS-84 can differ by hundreds of meters (I think) in some parts of the country, so the distinction does matter. Now you can see the wisdom of defining state borders by traditional markers rather than the currently popular geodetic datum...
There are formulas and webpages to perform the conversions, such as on the FCC website. They maintain some of their licensee and antenna databases in WGS-84 and others in NAD-27, all to make life more interesting.
