Biggest suspected problem, with tumbling live ammo, is breaking down the powder kernals. This would theoretically increase the surface area of the powder, which theoretically would increase the pressure. I'm not saying it does, or it doesn't, just this is the main reason why people say not to do it. I don't think that anyone is figuring rounds bumping into each other will start to set each other off.
ETA, use your own common sense to decide. Remembering, of course, that crates of ammo get transported in trucks and jeeps, through jungles and across deserts, in places that might not always have the smoothest roads. So perhaps, a bit of tumbling, may not be the most extreme thing you could do with it.