Special rank one groups are perfect

T. De Medts, Y. Segev and K. Tent [Special Moufang sets, their root groups and their \mu-maps, Proc. Lond. Math. Soc. (3) 96 (2008), 767-791] proved that the little projective group of a special Moufang set M(U,\tau) is perfect provided that U has size at least 4. We give a short, elementary and self-contained argument, working with Timmesfeld's concept of special (abstract) rank one groups with arbitrary unipotent subgroups [Abstract root subgroups and simple groups of Lie type, Monographs in Mathematics, 95. Birkh\"auser, 2001].