BOAC, either "track" is an area of best probability X nm wide. Depending upon the angular precision, and the number of "degree circles" it may have crossed, the thickness of that band looks to me to get into a few hundred miles either side of the theoretical center. I don't like thinking of those arcs as a "track" but as "areas of probability" that have variation between estimated points/times.
I did a little back of the napkin math. One degree of error or imprecision is in the range of 600 nm.
I am on board with your raised eyebrow regarding such a coincidence.