Well, I think, that the illocutionary mode of a command, which is represented by {ko}, {ko'oi}, {e'o}, {e'u}, and perhaps some others I might be missing, is not a statement saying "this proposition is true"; rather it's a command or request to "make this proposition true".
Thus {ganai broda gi ko brode} works, because if broda is false, then the listener does not have to do anything to make the proposition true; it's already true. While if broda is true, then the listener will have to do brode to follow the command/request. (of course, they may choose to not obey the command/request for whatever reason, but the meaning of the command/request is still clear)