The term 'support counterfactual definiteness (CFD)' is a bit vague. Let's interpret it as meaning that, in that theory, no contradictions with experimental results are derived by assuming CFD.
Bohm's Pilot Wave theory can allow CFD without contradicting the experimental observations from Aspect et al, because it does not assume Locality. Bell's paper assumes CFD and Locality and derived inequalities that appear to have been violated by the Aspect et al experiments. So either CFD or Locality has to be discarded.
Bohm's theory discards Locality - by allowing the hidden variables to be global, rather than local to the particles in question (the information is contained in the pilot wave) - so it can keep CFD.