The existence of Rule Zero in a role-playing game, or any of its other equivalents, does not invalidate the existence of any other rule. Rule Zero is roughly Referee Fiat – the idea that the referee has final say, and any content of the rules-text is subject for hacking, removal, addition, etc. by the table.
There exists a certain kind of role-playing snob who upon seeing anything akin to Rule Zero to proclaim “Then why am I buying this book, shouldn’t you have designed a system?” While ignoring all the tools, procedures, adventures, monsters, or any other useful material in the text that a referee may opt to use.
Like Jim P says “Rules are not bad or dumb” – they’re a tool to for the referee to help present the world and to determine what happens when rulings fail or the ref doesn’t feel like making one. Rule Zero should be an assumed default in every traditional role-playing game, and even if its not – no designer holds power over your table should you add it in.
Rule Zero is there to aid your gaming and leaves you free to utilize anything else in the rules-text to make your game run how you want it. It does not obviate anything that comes after. It just allows you to examine those rules as they come up and decide if they are really serving a purpose.
To do something that does not make fictional sense just because a rule tells you to do so is a betrayal of the medium of role-playing. The beauty of the game is the conversation – we can discuss, negotiate, and use our understanding of fiction to shape the imagined world. A slavish adherence to mechanics that produces fictionally incoherent world negates the strength of this hobby.
So Rule Zero is always on the table, and it allows you to use whatever rules you want to produce the game that’s right for your table. Just because you might change some things, make rulings on the fly, or even throw out sections does not mean what you keep and use does not have value.