You're making a bunch of assumptions here, the biggest of which is that the DM has somehow changed the parameters of this deity between char-gen and now (maybe even intentionally, in order to hose the player/PC); which I agree would be bad form if thusly done.
You are mistunderstanding what construes an assumption. It's not an assumption to raise the possibility that the DM and player may not be on the same page regarding the PC's deity/patron/oath when initiating play and that this can only become obvious later into play. An actual error of assumption in this case would be assuming that the DM and player are on the same page when play begins. And my comment was directed towards this egregious assumption.
I guess that begs the question of whether the patron is an aspect of the character or an aspect of the DM's world? I would say the latter and thus wonder why the player would get to dictate that...
To answer your begged question, I would say "yes" in the sense that it's obviously both. And here we may also point out the obvious that the PC by virtue of participating in play is also an aspect of the "DM's world." Nevertheless, players often tacitly mold the DM's world. When the player establishes as part of their backstory "my character was raised by his blacksmith mother in the town of Heretown," the player has now dictated something about the "DM's world." Heretown may or may not have existed before the player created their backstory, so this too may have been created for play. The character's mother exists in Heretown, and there is a smithy there where she works. Though this may remain subject to DM approval, the player has effectively dictated an aspect of their character and the world that the DM facilitates.
IMO this isn't wanting to explore the relationship from a character-side perspective but instead, akin to wanting to play out lone theater and/or dictate a story in a cooperative game by ones self..
So they want to create and control not only their warlock but also the patron he or she made a deal with.
I hope you don't mind me cutting the rest, but given how the rest of your paragraph follows from this gross misreading or mischaracterization, then it may be best to nip this at the bud. So let us first go back to what I said, and I will do my best to clarify my position better for you. And hopefully then you can respond in a manner that better respects what was actually communicated.
They may want the pact relationship as a warlock, but not want that as a prominent narrative element, but, rather, one that informs their decision-making for the actual primary issues of the campaign. They may not want, for example, their patron popping out of the narrative bushes and dictating new terms of agreement on them, betraying them, operating in ways that the player believes mischaracterizes the patron or their relationship, etc.
I am not suggesting here that the hypothetical player here wants to engage in one-man theater. I am arguing here that the hypothetical cleric or warlock are people who want to explore engaging the world and their themes through a particular lens.
Let us take, for example, a cleric. The cleric has faith, tenents, and likely a code. The cleric can explore their faith without the deity ever once showing up into play or the DM even dangling that possibility. The idea that a deity must or should show up in order for an adherent or priest to explore their faith strikes me as offensive and non-sensical from any real life sensibilities. In many respects it is the default position of the human perspective. Gods in D&D can be real and embodied (e.g., Forgotten Realms), but this is not always the case (e.g., the Sovereign Host in Eberron). And likewise from within the worldview of many religious adherents, the supernatural elements that constitute their faith (e.g., God, gods, spirits, etc.) likewise are regarded as real. And I believe that players, in my case at least, often do prefer playing from this human perspective over against one in which the deity exists as an NPC who exists as the DM's sockpuppet and for the sake of the DM's desire to "control all the things." As a frequent cleric player, I am often completely uninterested, if not turned-off, by the DM using my character's deity as an NPC for micromanaging my character.
Recently I had been playing a dwarf cleric of the forge in a campaign coming to a close. The DM has been entirely hands off with my deity. I established the fiction of the deity from scratch. I created a dwarf creator deity, loosely based on Moradin, who had male and female aspects: a male aspect of labor, crafting, and commerce (weapon: hammer) and a female aspect of agriculture, family, and brewing (weapon: sickle). I established my character concept as essentially a revolutionary pro-labor, socialist, Communist dwarven priest. Exploring my character's faith is built into the themes of the campaign and how my character with their particular religious ethos engages the adventure setting. My character and his barbarian sister (another PC) immigrated to a frontier "new world" colony across the ocean that also serves as a penal colony. My character has been engaging this setting from the perspective of their faith. How should a pro-labor and anti-slavery priest feel or respond to issues surrounding the penal colony? How might a revolutionary, heretic priest make a fresh start for his cult in this New World? What are objectives that a pro-labor priest might want to achieve to improve the conditions for working class laborers in this colony?
The idea that I am therefore somehow playing "lone theater" or that I am incapable of having other players/the DM see my decision-making process or the influence of my faith is not only downright insulting but also contradicted by actual play experiences. Just because my deity is "absent" or removed-from-play as the DM's plaything does not mean that my character and their faith exists in some sort of vacuum. It engages the world. My character's ethos and faith has been the most well-defined, grounded, and consensually understood among the group. It has made my character a moral beacon and pillar for the group. My faith has vocally informed many important decisions that my character has made. If the DM wants to explore my faith, they do not reach their hand up the deity as a sockpuppet; they establish human situations and scenarios for my character to engage. I am not running amok and abusing power without any responsibilites; those responsibilities are accumulating. And I wanted to engage those responsibilities as part of how I envision the character. I have established contacts, begun reforming prisoners, laid the groundwork for coordinating the guilds, and laying the foundations for a chapel and future temple.
This is similarly what I have in mind in my above paragraph. A player character is more than capable of exploring their religious devotion or arcane patronage without requiring the in-game intercession of the NPC or the DM's control thereof.
Could you explain how the DM playing an NPC (because that's what a patron or deity is) can tread on the concept of the actual character?
This is an incredibly broad question, and one that has been discussed before numerous times already. Given the broadness of your question, it may be more conducive for discussion for you to consider and answer why you might believe that would be the case. I am asking you to extend yourself out of your own comfort zone and preferences for a second. Scary, I know. Why might others who are not you or your group feel, think, or believe that based upon their own experiences in play? Are there circumstances that you can consider where the DM's play of a backstory-related NPC could encroach, tread, or impair a player's PC concept?
And if that is the case why doesn't it apply for any other NPC the player's characters have a connection with?
I believe that it can, and often does, apply to other NPCs the PCs have established backstory connections. We have been discussing the issue primarily in terms of the warlock and their patron (and the similar cleric/deity relation), but the issue has also been raised in terms of other backstory-pertinent NPCs that a player may want "backgrounded" for their character (e.g., family, animal companions, etc.) to varying degrees.