Of course you are. That's not the relevant part to what I'm saying, though.
The rule itself is not saying that you the player are the one who can declare fiction, though. The rule simply says that a PC can only have 1 class at level 1. It applies equally to both players and DMs creating NPCs with PC levels. There is no inherent distinction in that rule about who dictates the fiction. That rule is not about WHO declares what is happening in the fiction. It's simply a tool with no statement about who uses it to declare fiction. It's neutral.
"YOUR FIRST STEP IN PLAYING AN ADVENTURER IN THE Dungeons & Dragons game is to imagine
and create a character o f your own. Your
character is a combination of game statistics,
roleplaying hooks, and your imagination. You
choose a race (such as hum an or halfling) and
a class (such as fighter or wizard). You also
invent the personality, appearance, and backstory of
your character. Once completed, your character serves
as your representative in the game, your avatar in the
Dungeons & Dragonsworld."
--D&D 5e PHB p11
Similar text discusses the other major choice, class.
An example of a rule that states who declares what is happening in the fiction can be found on page 174 of the DMG.
"For every ability check, the DM decides which of the six abilities is relevant to the task at hand and the difficulty of the task, represented by a Difficulty Class."
If a rule does not dictate who decides, it is not a rule about who specifically is declaring what is happening in the fiction.
See above.
It's written, at least in D&D, as Rule 0. I think why it's viewed as unusual in some other systems by some people is that D&D was first and that colors the views of people who started with D&D. I don't think a group who starts with one of those newer systems would view it as unusual.
It is not something which exists in games like Apocalypse World. If you come to RPGs through one of those games, you will find rule 0 to be odd and unusual.
In D&D it's spelled out clearer than that.
The How to Play rules on page 6 state that...
1) The DM describes the environment. This includes the village of Ardun and the existence of the chief militia officer.
2) The players describe what they want to do. This would be when the player declares, "I walk into the village of Ardun and speak to the chief of militia."
3) The DM narrates the result of the adventurers' actions. This is when the DM determines(presumably via rules, notes and/or whatever else) whether the chief militia officer wants to talk to the PCs. This is also the beginning of the new step 1 as the environment has changed slightly with the narration.
Then the process repeats with steps 2 and 3. Over and over and over.
Which rules come into play on the side of the player and/or DM(if any) will vary with each repetition of the play process. Some rules will be player facing(declaration of PC actions) and be about how the players are the ones that are determining what happens in the fiction. Some will be DM facing, such as the DC rules and will be about how the DM is the one who is determining what happens in the fiction. The vast majority of rules, though, are PC/DM neutral and are not about who determines what is happening in the fiction, but rather are used to help figure out how the few other rules that are about who is determining what is happening in the fiction are resolved.
Can you describe some of these?
For example. The rule about the player declaring what his PC does is enacted by the player to affect the fiction by saying, "I walk over and try to climb up the back of the building to get onto the roof." The rule about the DM deciding DCs is enacted by the DM to affect the fiction by the DM saying, "Okay, it will be a DC 15 climb check." The rule that allowed the player pick proficiency in athletics was neutral about who decides what in the fiction, but is consulted to help figure out the resolution.
I see no such passive construction! For example, PHB P47 describes the Barbarian class (and remember above that picking a class was actively described as a player choice) skills are mentioned as "
Skills: Choose two from Animal Handling, Athletics, Intimidation, Nature, Perception , and Survival." This is pretty conclusive! The player is also described as selecting her ability scores, and thus ability bonuses, etc.
Hopefully that makes what I'm saying a bit clearer.
I am not sure what it does. I don't doubt that SOMEWHERE in the corpus of D&D 5e there's some text that is neutral and to whom it is directed can only be ascertained by construction or context. I don't think this makes the point you think it makes. I think it is merely writing style, possibly in some cases combined with a desire for efficient design (IE not saying the same thing over again for different contexts).