Ender Dragon can still grief stuff like cobblestone and chests even if the gamerule mobGriefing is set on false.

Ender Dragons can still grief stuff like cobblestone even if you set the gamerule mobGriefing on false.
You can check that on a new world on creative, and getting on the end. When you put a 1x1 cobblestone tower, then when the Ender Dragon comes to attack you, it breaks the cobblestone. You can also try it out placing a chest. Then the Ender Dragon will break it.

PD: The texture pack I was using was a customized version of Dokucraft The Saga Continues.

PD2: I think that affects to every gamemode.
PD3: Ender Dragons can remove water and lava.