Let me try to clear it up. (sorry, it got a bit long)
First, the skin (and skull and clothing .. etc.) does act as a barrier, which is why the graph that is shown in the article is flawed (this is mentioned). It shows absorption of microwave radiation in the grey matter of the brain, but it doesn't account for the skin and skull that blocks it.
There are two major effects of radiation: ionization (think X-ray imaging) and heating (think microwave oven). Ionization is irrelevant for 5G, because the frequency is way too low. Heating, on the other hand, happens at many frequencies. For example, a microwave oven is at ~2.4 GHz, just like Wi-Fi (which can also operate at 5 GHz).
That said, the heating is dependent on how much power is transmitted and how well it is absorbed by the skin. For example, a low-power source (Wi-Fi antenna) doesn't fry your skin like a microwave oven because a) the power is too low and b) it mostly reflects off the surface of the skin.
The power levels that 5G needs to operate at are quite low and the reflection off the skin is quite high. This is summarized nicely in the reference I gave in another comment here [1].
To answer your specific questions:
> So am I to understand 5G causes merely skin cancer, not brain cancer? Or is non-ionizing radiation safe regardless of shielding?
The ionization effect is not present due to low frequency (see above), the heating effect should be considered, but is minimal (see reference). The authors of [1] note specifically that the skin area is safe, but the eyes may be more vulnerable if the devices operate at large power and are close-by. So, this is not dangerous for consumers but may be dangerous for workers near antennas. However, the radiation level must be very high, and the distance very short. In my reading of the paper, it is not a danger for commercial telecom applications.
> Would it be too much to ask for blasting a few thousand rats with 5G?
That is not my field of expertise..
[1] https://ieeexplore.ieee.org/abstract/document/7032050