The configuration file states that disabling ownership does not affect the Carpenter's Safe. Despite this the safe can be opened by other players if it has been locked (red light showing) if ownership has been disabled. Activating ownership again immediately returns the safe to expected behaviour.

I have disabled ownership as I like the idea of beeing able to build and modify something in cooperation. But having a lockable storage is also important to me.

I have tested this on Carpenter's Blocks 3.3.4 using Forge 10.13.2.1272.