C-4 needs, as mentioned, pressure and heta to detonate. A rifle round won't do it, a nearby explosion sometimes will... I have seen it not explode from some field expedient priming attempts.
I am not sure what type of priming system that the MLRS uses, but unless the rotations trigger a mixing of chemicals or actually move the initiator into the C-4, I would suspect that the initiating explosive(which would be much easier to create a sympathetic detonation in than the C-4) would be subject to detonation upon small arms impact, and would the initiate the C-4.
So in a way they would be correct, the C-4 won't go off from a small arms hit or most grenade hits, but the initiating charge would... and that would set off the main charge.
This is just my best guess based on my military experience playing with C-4 and other explosives, since I have no direct MLRS experience. There are a few EOD types here, they may be better able answer your question.