If you use the ruler to directly measure the distance between subsequent points, the random temperature fluctuations will be as likely to increase as decrease t

If you use the ruler to directly measure the distance between subsequent points, the random temperature fluctuations will be as likely to increase as decrease the measured distance (of course for a real steel ruler, this would be dominated by the systematic error in the ruler's markings, which will accumulate over summed measurements). If instead you used the ruler to measure (X, Y) co-ordinates of each point, then calculated the displacement between the points from those co-ordinates, the random errors would have a bias towards lengthening the path as in the article.