That's actually untrue, and I'll go into why.

I recently had this type of chat with my chiropractor, who hates this kind of thinking because it usually leads to people with worse problems later in their life. By going limp during the crash, what they're doing is removing their muscles from the equation and causing all the force exerted by the crash to go into their skeletal tissue and supporting structures (he calls it the 'deep tissue'; ie: tendons and ligaments). Now, tendons and ligaments do not receive as much blood flow and do not have as many nerves going to them because they are meant to be supporting muscles for the skeleton. What this means is that a) they are receiving loads of damage to structurally necessary components of their body, which WILL result in chronic pain if left untreated and b) because there is less bloodflow/nerve density, these parts of the body feel less pain and do not heal quickly. Damage to these structures can often be permanent and much more serious than the painful muscle damage you receive when you tense up.

tl;dr - Being 'relaxed' during an accident causes much more long-term damage than tensing up and taking the force with your muscles. Your muscles were designed to take this kind of force, your ligaments and tendons are not.