You are correct that all cartridges put energy into the arm- this is how the arm moves across the LP after all.
The trick in the setup is such that the information is transduced by the cartridge rather than applied to the arm tube. This is done by setting up the proper effective mass, which has nothing at all to do with the materials of the arm as long as the resulting mechanical resonance falls within the target area. IOW the last sentence of your first paragraph in the post above flies in the face of tone arm theory in general.