Yes, to me rejecting objective meaning is nihilism, what do you call it? What you call nihilism, i might call radical nihilism or extreme nihilism. Yes, taken to the extreme, it would lead to total apathy, as there is no reason to do anything (Also no reason to kill yourself btw). But you can still have nihilism as the foundation of your philosophy. That would probably be a contradiction to you, cause you take nihilism very literal. And yes, by your definition any known nihilist is a fake nihilist, otherwise you wouldn't know them.