Generally it seems to make sense, that grease should have the same depth compensating effect as oil.
On the other hand I have never seen a diaphragm 1st grease filled.
The only idea I can come up with, is, that only liquid can guarantee to generate an even pressure on diaphragm and especially the spring pad and so the pin support which resists on a flexible area ( the diaphragm) and a small rigid area ( the spring pad) the main spring pressure.
Probably will just small imperfections in grease packing have a less secure effect on that mix of materials than on a rigid metal piston to secure the pressure adaption to depth.
If you point the ambient pressure with a plastic piston right on the spring pad (and spring support), like on the Conshelf ‘Dry’ Environmental Kit, you don’t need the diaphragm area to support the pressure on the spring pad.
I’m sure that in practice a grease filling also will work, but maybe not as reliable as liquid fill.
Hope I could make my thoughts understandable also in English.