This is untrue.
Any conducting material with grid spacing significantly smaller than the wavelength of the signal to be attenuated is a Faraday Cage.
In particular, a metal box with thickness greater than the skip depth of the wave (which is no more than 100 microns or less) is always a Faraday Cage.
Grounding is required to avoid damage to objects outside of the cage, because induction currents induce charge on the outside of the box, which can be quite large if the signal has high energy. It does not affect the effectiveness of the cage as a shield. [I have demonstrated this to undergraduate physics and EE students, many times.]
Did you read my follow-up post #58?