Spinning particles coupled to gravity

Recent experimental work has determined that free falling $^{87}$Rb atoms on Earth, with vertically aligned spins, follow geodesics, thus apparently ruling out spin--gravitation interactions. It is showed that while some spinning matter models coupled to gravitation referenced to in that work seem to be ruled out by the experiment, those same experimental results confirm theoretical results derived from a Lagrangian description of spinning particles coupled to gravity constructed over forty years ago. A proposal to carry out (similar but) different experiments which will help to test the validity of the Universality of Free Fall as opposed to the correctness of the aforementioned Lagrangian theory, is presented.