Grenades have this nasty tendency to bounce and just go everywhere...like a pinball. By the time you get your hand on it, it's been cooking for probably at least 4 seconds on a 5 second fuse.
Now, I would recommend jumping on a grenade, about as much as I would recommend hooking jumper cables to your scrotum (actually, there's a few I would love to do that to, but I digress...). Anyway, sometimes there's no time to do anything but just lay down and scoop it under you.
Enemy grenades DO get thrown back. But you don't read about those on Facebook or in the news...