A GM should never, ever change your backstory.
Developments building off said back story, however...
I am sorry, but I disagree. In my mind, a character's back story is a cooperative effort by both the GM and Player. I would never give a player carte blanche for creating his character's back story as there would likely be elements that would conflict with my campaign.
For instance, when one of my player's made up a recent character, he wanted him to be the son of a very wealthy merchant whose parents met a terrible demise and the son was left to be raised by an uncle. While that in itself is a very acceptable idea for a back story, it would mean that I would need to incorporate a new wealthy merchant family and company into the history of a city that I had already developed around a story arc (and I really did not want to have to redo that work). Instead, I asked the player if he would be OK with his family being up-and-coming merchants on the brink of making it from lower class into middle class. He was OK with it and in the end, we came up with a nicely defined back story that had some good flavor, intrigue, and a number of unanswered questions as to what happened to his family and his families holdings. He was quite happy with it.
Also, there were several elements of his back story that were explained in one way that I had planned to actually mean something completely different due to information that the character was not aware of. There is nothing wrong with that.
I don't see why any of this required changing the character's backstory.
It wouldn't have required "introducing a new merchant family". They're all dead. There USED TO BE a new merchant family, and now there's not. Where's the conflict?
Even if they were still alive...so? It's not like it changes anything significant in either case. It is literally just a matter of erasing the current number you have written down and writing in the new number. What "work"?
It's good that...
I kind of agree with Rynjin, but I can see the warning flags of that backstory too. It really boils down to 'what was the player going to do with it?' Was he trying to sneak some kind of mechanical/RP bonuses into the game?
If the adventure involves the PCs leaving town and riding across the country, then it really didn't matter one bit if there used to be a wealthy family that was magically inserted into the city Heirarchy.
If the game was going to be BASED in that city... and the PC was planning on using his parents friendly contacts and access to some extra money, pity from people who knew his family, and/or intricate knowledge of the shipping/trading industry... because he's awesome that way... Then yeah, I may have wanted a few tweaks to it as well. I get a little nervous anytime I hear 'Wealthy' or 'nobility'... unless the game was designed for it. They're just red flags for me that someone's looking for a bonus somewhere.
Which brings me to another point.
One thing that I think is very important when designing characters and backstories is that you are also in some ways directing the DM. I can say that I have never collaborated with the DM on a backstory yet. I write it up (usually a few pages long) and then send it to him for fun. He's never vetoed anything yet. However, I also don't try to run roughshod over their world either.
If you create parents... The DM is expected to play those parents. If you create an organization, the DM plays the organization. If some cult or bandit leader or something doesn't make sense... The DM has to figure out how to make it work with the world he already has... If you claim to be a lost prince of the country... sometimes the royalty has already been planned. The choices are either A) Your story is ignored or B) it is shifted a little. Especially when people want to play weird or forbidden races. Now the DM has to play all the OTHER catfolk or Drow and deal with any racism or persecution that he really didn't want to deal with. However when a player choses 'drow'... there's an expectation that certain Roleplaying aspects will be there.
Most of the time I've seen DM's WANT to work your stuff into a game. It makes the game more fun, more personal/memorable, and more engaging for the players. So try to make things that are easier to work with. Instead of being mayor of a town. Be a cobbler. Some things are easier to switch/add then others.
My standard way of making a character is this. Create the character I want to play. Figure out his age... consult timelines to see what he lived through (easier in established worlds). Look at skills/feats. Explain where they came from. Create three allies, Create three enemies. Work into coherent story. Hand to DM.
Some of it tends to get pulled into a game... some of it doesn't. Having options like that mean it'll be a surprise which thread happens ;)
I mostly homebrew when I get a chance to play these days. I make sure to give particulars of how I want to start the 1st campaign that brings them together. We all have a get together and decide what country they want to be from and the classes they want to play. I give them any relevent information on the particular town/city they are from such as ruler of city, the guards standards if any, a few shops/inns/taverns they would probably know about etc. This way they could build their pc with a few extra flavor things.
I think collaboration is important and wouldn't change a backstory unless it was something that would be completely disruptfull. I haven't had to do this thankfully.