This study is on very shaky theoretical ground. One major issue is the author doesn't seem to understand how atmospheric conductivity works. It is dominated in the ionosphere by the mobility of heavy atmospheric ions (H+, O+, etc.) and free electrons. Adding neutral (non-ionized) metals can actually serve to impede overall conductivity, because it increases the collision frequency between the charge carriers and neutral atoms/molecules. Thus, less current can actually "flow" before being dissipated, leading to higher (not lower) resistivity there.
Further, they argue that the magnetic field outside of a conductive layer of metal fragments containing the Earth is zero. This is only possible if those fragments can carry a strong global-scale electric current. But they are not a wire or solid piece of metal as the author envisions, rather just isolated fragments that cannot transmit a current to each other without again colliding with the neutral atmosphere. In reality, any small/finite amount of electrical resistivity will allow the magnetic field to diffuse through over time, which certainly would happen here.
They also compare with mass loading from the radiation belts, which is silly, because it is well-known to be a very low density region that precipitates very little mass. The primary ionospheric mass loading sources are typically ions from the nightside plasma sheet (responsible for many auroral phenomena) and the polar cap, where solar wind ions can directly penetrate Earth's field. These number fluxes are orders of magnitude higher than the radiation belts, and should have been compared with instead.
I could go on, alas...