I'm still not sure that's true, but what about the other bit of my question - does it contribute to the weight if the cabin is not enclosed/pressurised (not sure which one of those is the significant one.) Clearly not, I'd suggest, as a moment's reflection on a bird sitting on your lap in a Tiger Moth will make obvious.
So what exactly is the difference when the cabin is enclosed/pressurised? I guess supporters of the bird-weight theory will say it's still the downdraft, but I have to say I found the response to my question as to what happens if the downdraft is artifically blown away by a fan unconvincing.
I also suspect that for the same reasons, some of you will say the Tiger Moth situation described above is not so simple. OK, but then the question arises as to how far does the bird have to go before it no longer contributes to the aircraft weight.
The significant part is the cabin being enclosed. Pressurization is not important.
Consider two aircraft in formation flight, or one flying and the other on ground. If the downdraft generated by one aircraft hits the other craft, the weight of the plane flying/located in the downdraft increases, because some of the weight of the other plane rests on it. But so long as both craft are in external airflow and not in enclosed cabin, both are generating some lift and their propwash or jet blast is escaping. Now, when an aircraft flies into the cabin or cargo hold of another plane and the cargo door is closed, its downwash no longer escapes the cabin, so exactly its whole weight is transferred to the other craft, whether the inside aircraft is hovering or resting on cabin floor.