I've heard that too, and think it does make sense, up to a point. Soft materials are compressible and thus can bend and return to their original shape. In this sense, a bit of padding (fat or even muscle) is better than just skin and bones. Additionally, the force an be spread over a greater surface area, lessening the stress on any one point. (Airbags are designed to do these two things.) However, greater mass means greater momentum. So as you are increasing this extra padding, you are also increasing the force you feel at impact (and also the force your safety mechanisms have to withstands, I've heard of the seats becoming dislocated by this momentum when passenger was super overweight.) This mitigates the advantage of "extra padding", though to what extent is the big question. Someone who knows the physic better would likely have a better answer for you.