  In the last few years, the so-called Chen et al. approach of the nucleon spin
decomposition has been widely discussed and elaborated on. In this letter we
propose a genuine differential geometric understanding of this approach. We
mainly highligth its relation to the "dressing field method" we advocated in
[C. Fournel, J. Fran\c{c}ois, S. Lazzarini, T. Masson, Int. J. Geom. Methods
Mod. Phys. 11, 1450016 (2014)]. We are led to the conclusion that the claimed
gauge-invariance of the Chen et al. decomposition is actually unreal.
