Does it though? At what frequency? In the limit of f=DC this is trivially not true.

Also, if that were the case, an airplane couldn't be made into a Faraday cage.

Also, the cage+Earth system would itself be an antenna.

If you need ground for a topologically imperfect cage, maybe… but I doubt it.

I think (but I don't know!) this is like the legends surrounding engine torque car guys believe. Electrical engineers putting everything to ground because they got burned