The Edit Terrain Object module only hides the buildings on the host. Clients get to see the rubble, but also the buildings that were supposed to be destroyed.

Pictures for comparison:
Host computer.
Connected client.

Tested on Stratis, Agia Marina, but problem has occurred everywhere used, including modded terrains like CUP Maps and Helvantis, as well as when hosted on dedicated servers, where the AI will use the rubble of inaccessible buildings while no one can see them.