We use microscopic many-body theory to analyze the problem of itinerant ferromagnetism in a repulsive atomic Fermi gas of hard spheres. Using simple arguments we show that the available theoretical predictions for the onset of the ferromagnetic transition predict a transition point at a density (kF a ∼ 1) that is too large to be compatible with the universal low-density expansion of the energy. We present variational calculations for the hard-sphere Fermi gas, in the framework of Fermi hypernetted chain theory, that shift the transition to higher densities (kF a ∼ 1.8). Backflow correlations, which are mainly active in the unpolarized system, are essential for this shift.