I think its like a can of soup with say peas in it (or a tin of beans for that matter).
If the can is sat on the scales with all the peas resting on the bottom of the can, it still has the same weight if you shake the can thus suspending all the peas. The soup supports the weight of the peas. The air in the cabin supports the weight of the parrots if they flap enough ! If one suddenly dies mid flap and falls on the floor, the plane (can) still has same weight.
If now you were to open the can of soup, take the lid off and shake it then weigh it I expect the can will weigh less (and you will be covered in soup).
Could be wrong
