Are we talking armed or un-armed grenades? I guess it doesn't matter.
1. Armed 40mm HE grenade hits you and shreds your body to pieces with shrapnel.
2. Un-armed 40mm HE grenade hits you like a 170 mph 2-pound golf ball, either penetrating in a soft spot, (e.g. stomach) or bruising and breaking bones in harder spots(ribs, legs, arms, head).
Get the picture?
I hope I don't sound harsh or anything; it's just that those rounds are heavy and moving fast. If you were hit by one you'd be pretty well incapacitated. So for the purposes of the game, you die.
If it's stupid, but works, it isn't stupid.