If it was loose the car wouldn't go anywhere.
Diffs distribute power to the easiest thing to turn. For example if you put one wheel on the ground and the other in the air the one on the ground wont move at all, but the one in the air will spin happily. With on-road all wheels are always on the ground.
So if you think about it offroad tracks are bumpy. So if one wheel bumps off the ground (or for whatever reason dosn't have full contact with the ground, which obviously happens a lot in off-road) all the power will be transfered to that wheel but not to the one on the ground and the car just wouldn't go anywhere fast. Also with loose surfaces the same thing applies so when there is less grip on one wheel it will spin more then the one with more grip. (which is pointless because it gives most power to the wheel with least grip)
This obviously creates a very in-effcient diff and will not only slow the car down but because of the extremley heavy usage melt it.
Thats why the diffs are tight to stop this un-necesary diff action. Whereas tarmac are flat and solid so on-roads have problems with bumps and loose surfaces.
Hope this makes sense