This isn't really my experience.
For instance, in my first RM campaign a player wanted to play a mystic whose childhood was spent herding sheep (or maybe goats?), and whose mentor lived in a large hollow tree and was in hiding, a refugee from some sort of mages' power struggle.
This is an example (more detailed, though) of what I call a generic background. Not that it's not interesting or lacking in hook, with an established NPC the player will care for and who might be in need of help (either because he'll be targetted directly, but that might come across as adversarial GM'ing to the player, or because his need to keep hiding will prevent him for doing certain things directly, causing him to ask help from his charge). That's great, but I can fit that as easily in Dark Sun, Forgotten Realms or Eberron: the prerequisite from the settings are only the existence of trees, animal husbandy and a conflict between wizards somewhere in the setting, none of whiich are outlandish. With existing knowledge of the setting, the players could have tied his mentor to a specific faction holding supernatural power, providing a reason to hide for the mentor and helping the GM to desing the first adventure.
In my first 4e D&D campaign, one of the players came up with a very intricate background for his dwarf PC, and another player a very intricate background for his refugee human PC, both of which established significant aspects of the setting.
In my first Burning Wheel campaign, one of the players established as his PC's overarching goal the freeing of his brother form possession by a balrog. There was also enough character backstory to explain the basics of how this possession came about.
I think that when players have these sorts of ideas/aspirations for their PCs, there is the possibility of a clash with the sort of detailed setting design advised in the RM books mentioned in the OP.
This two examples are interesting and I see where the conflict might be. In your OP, you mentionned "what if the idea of the character schooling clashes with the seting?" Let's imagine a player who imagine being from a large city, attending an art academy, and going out to see the wonders of the world to find inspiration for writing the greatest epic ballad ever and be crowned Prince of Poets. Problem, in the setting design, the GM had decided upon a pre-agricultural world, with hunter gatherer tribes wandering the land instead of a "more traditional" faux-middle ages. How to reconcile these?
First, establish what's important for the player and the GM. In both the setting and the background. I am partial toward communal character creation during session 0 and I ask the players to include a reason to actually work with the other players (to avoid the "why exactly should I care about the destruction of the city by an evil lich? I am a wood dwelling elf for Corellon's sake!" problem). This is also the occasion to distinguish "red lines" and things that can be changed. In your example with the cursed brother, maybe the clash would be with balrogs (because in your setting idea, they don't exist, say) but the player would be happy to replace balrog with the Wild Witches of Woe that you established as an evil power group in your setting, or maybe the balrog thing is very important and you didn't plan of having balrog but don't object to them being in the setting (potentially made to fit by being invoked by the Subterranean Sorcerers of Slaughter that you also described in your setting. The tension only subsists if "red lines" collide, and not everything in the background or setting is "red line" material.
Let's imagine the character concept of the urban bard is all "red line" to the player of the example about schools
Solution 1 : DM caves in, and suddenly there is a capital sitting in the middle of the pasture. This is a setting defining change. How does it survive without farming? Does it taxes hunter gatherers (ransom would be a better word)? If they can do that, it means they can threaten everyone around them... are they governed by a council of powerful mages that could drop asteroids on the surrounding tribes if they failed to supply appropriate tributes? Resolve those with the players: will he accept to be from a distrusted, exploitative metropolis whose name is spoken with a mix of fear, hate and wonder by the rest of the setting? If not, will he accept to be a stranger in a strange land, having just arrived from a fabled continent (that wasn't detailed in the setting) so the city can be from a farming culture far away from the setting center? There are refining opportunities that can make it work, if the GM has detailed only a partial setting. I concur with the advice given above not to detail 100% of the setting, to make way for some adjustment and enables this type of solution.
Solution 2 : players caves in. If given an overview of the setting and seeing all the other players are creating background from the Three Bear tribe, he'll change his idea and make his bard looking to explore the world an idea for another time, or retrofit some themes to mesh with the other players and the setting. This will be easier if he's knowledgeable about the setting and sometime this solution is implemented before a tension can be seen, because the imagination of the player will take into account the limit of "this is an hunter-gatherer setting with neolithic technology, I can't be a smith's daughter!".
Solution 3 (the worst, but sometimes unavoidable): the road block. when everything is red lines, because the player not only imagined his bard, but also seventeen collegues studying at the bard academy, five teachers feuding with each other over minutiae as only academic conflict can, an twenty-three family members and dependant all livingin the city? Well... then it's probably not the campaign to be in this time. It's not necessarily a failure. Everyone is there to enjoy the game, and if enjoyment can't be found in the shared story to be told, sometime the best way is not to be part of this story. If one doesn't like super hero and the DM wants to run Mutant and Mastermind, there is no solution.The same divide can appear within a genre sometime, but it's rarer. In my experience, it's not often that a background will be impossible to fit if both parties (GM and player) are actively looking to compromise. Solution 2 can happen naturally, solution 1 can be implemented if the world isn't 100% described (and it's never the case ; it's more often a sign of a DM inflexible in his view of the setting...) but if both sides are set in stone (let's say because the DM wanted to have the player be the one to be the first to bring agriculture and cities to their tribe, becoming worshipped as the creator gods ever after, and the player was dead set on hailing from a very common urban environment) and they won't find both enjoyment in the changed story, then one of them should leave (usually the player if he's the only one not interested in the prospective story, sometime the GM if his setting is so constraining that players all fear a railroad).
