You'll need to read the actual paper (as opposed to the above description of it) to understand that what the paper proves is for a particular type of trajectory (consisting of only straight lines between GPS samples) and a particular method of calculating distance traveled (the summation of its estimates of those straight line distances, or simply connecting the dots), a GPS it will always overestimate the true distance.
A simple example of this is if you walk in a straight line carrying a GPS. Each sample it takes as you walk will probably be slightly to the left or slightly to the right of where you actually are. If it calculates distance by simply connecting those dots, that path will always be longer than the straight line path that you took.
But GPS units don't use this method of simply connecting the dots to calculate distance. They use filters to smooth out those dots because they know, for the most part, people don't run or bike in zig-zag paths. They tend to follow straight lines or smooth curves, so the GPS filters the data to approximate the straight line or smooth curve that you probably followed, and calculates the distance of that smooth path. Of course that estimate of your path is not perfect. Sometimes it is slightly longer, and yes sometimes it is slightly shorter, than your actual path.