All this talk about the definition of what Fog is and what Hill fog is and whether they were VFR or IFR is irrelevant. The weather could have been Blue-Blue and they could have still been IFR.
The question is, were they VMC? Were they clear of cloud and in sight of the surface and the answer is clearly No. They were IMC and below their Safety Altitude. They should have turned around.
They were unprofessional and displayed poor airmanship - but they were not grossly negligent.