That just looks like that from the angle of the camera. When I remember the hand grenade manual correctly safe distance for a hand grenade for troops in cover is 1m, so he's good. Since in those times they still used the hand grenade 43 it was probably without the fragmentation ring around the grenade. So it looks more dangerous then it actually is. It's fun anyway. I miss those times.
During basic training and NCO school we had hand grenades, machine guns (M2 12.7mm) and Panzerfausts. In the repetitions courses all we had was machine guns and pepper sprays. No fun at all.