Many young and intermediate age massive stellar clusters host bimodal distributions in the rotation rates of their stellar populations, with a dominant peak of rapidly rotating stars and a secondary peak of slow rotators. The origin of this bimodal rotational distribution is currently debated and two main theories have been put forward in the literature. The first is that all/most stars are born as rapid rotators and that interacting binaries brake a fraction of the stars, resulting in two populations. The second is that the rotational distribution is a reflection of the early evolution of pre-main sequence stars, in particular, whether they are able to retain or lose their protoplanetary discs during the first few Myr. Here, we test the binary channel by exploiting multi-epoch VLT/MUSE observations of NGC 1850, a ∼100 Myr massive cluster in the LMC, to search for differences in the binary fractions of the slow and fast rotating populations. If binarity is the cause of the rotational bimodality, we would expect that the slowly rotating population should have a much larger binary fraction than the rapid rotators. However, in our data we detect similar fractions of binary stars in the slow and rapidly rotating populations (5.9 ± 1.1% and 4.5 ± 0.6%, respectively). Hence, we conclude that binarity is not a dominant mechanism in the formation of the observed bimodal rotational distributions.