The idea is to put it down on something with a bit of "give". Mattresses or pillows would do a similar job to take up the shape of the underside of the aircraft, so the least damage is done. You probably cant avoid bending the odd pipe or antenna, but you dont want to find that because of the C of G position, or the slightly uneven ground under the grass etc that you have trashed too much of the fabric of the aircraft.
Also, you want to reduce the chance of the aircraft rolling over when you shut the rotors down. I guess any slight rotor imbalance is going to feel magnified when you land on the solid belly of an aircraft rather than an oleo strut or a flexible skid.