The point has always been that the more the DM flatly decides the less agency the players actually have. If a rule doesn't do what it says it does solely because the DM so decides that is a pretty explicit removal of player agency. It is absolutely reasonable for the people playing the game to base their decisions on the rules of the game they're playing.
Right, but that falls into the realm of bad DM'ing, which might or might not include player agency.
I'll stick with the Noble Background, since that is the "rules" that are being discussed. Part of the rule says this:
"Work with your DM to come up with an appropriate title and determine how much authority that title carries."
Another part, which is specifically being talked about is: "Position of Privilege: [snip]. You can secure an audience with a local noble if you need to."
Those are tied together. If the player hasn't worked with me, as the DM, to establish who their character is, what their position is, how it applies in this realm/kingdom/whatever, and what their social standing is, then I have nothing to work with in terms of how the NPC "local noble" is going to work. Do their families get along? Is this local noble lower or higher status? Is this local noble the Duke? Are they busy? Are they accessible to everyone all the time? How does this play into the campaign/game that has been established?
Without that kind of background, I can't adjudicate the interaction/encounter.
A player in my game wouldn't have the noble background without discussing what it means, and what access and power accompanies it. Then, I know how to implement such requests.
As an example, I'm running a sandbox in Greyhawk, using the Beyond the Wall Rules. The party is 4 PC's at the moment, one is the son of the local Blacksmith, another is the daughter of the local Baron (Beyond the Wall doesn't have backgrounds, per se, but the Playbook the character was created under leaned in this direction, so we leaned further into it), a third is the son of a disgraced noble house, whose lands were lost in the recent war due to the family fleeing; the fourth is the second son of a noble house allied with the second character's house.
They all have backgrounds, which talk about their houses, their house relationships, the relationship of those houses to the Marchioness and other ruling houses, etc. The characters are free to do whatever they want and go wherever they please. That does not mean that they can decide to adventure with the family's men at arms in tow, or willy nilly spend the family's money, or have an endless supply of horses, or even supplies. But their names and titles carry weight with other families (some, not others), local knighthoods, etc. They invite dignitaries to their home for meals, they make deals on behalf of their parents (which the parents often don't know about), promise to provide supplies to far flung outposts (again, which are nobles promises, but no guarantee of being fulfilled, that's up to the players), etc.
Often I see "player agency" thrown around as code for "I can do what I want and the DM can't say no." That's not really how a game like DnD works, or has ever worked. Sure, some things like spells, and attacks do, but anything exploration, social, survival, etc. has often required working together at the table to adjudicate it, with the final say falling on the DM. And if the DM is just saying "No.", that's a DM issue.
If a player in my 5e game, playing a Noble Background, wanted a meeting with a local noble, I'd need to know for what purpose, and what they hoped to accomplish. Which would be weighed against that character's reputation/renown in the area, how busy or approachable the local noble was, what the local noble would look to get from the meeting, etc. At a minimum, the character would approach or have "their people talk to the local noble's people" about setting up the meeting, etc., making sure all the noble proprieties are properly followed. Then a "Yes, and or but..." or a "No, but..." or "No, however..." Then its up to the player to play it out - follow up and push for the meeting, forget about it, jump through hoops, etc. But its all up to the player. Its never "No." End of.
