How about if you're the player and the GM says: "OK, you believe you were posssessed by a god."
Do you say:
"No! I definitely was possessed by a god! No funny business mister!"
Though I take your point about the bait & switch, and I would be reluctant to do this to a player character in a way that seemed disrespectful to the player.
OTOH, this 'contract' approach was exactly what got the unkillable-PC player booted from my game last December - he'd sent me a multi-page background, poorly written, I'd glanced at and signed off on. When his PC died he emailed me after the game and said that the bit in the background about his family being cursed to be killed by a red dragon meant a contractual obligation on me that he could only be killed by a red dragon. This wasn't the first attempt to pull crap like that on me, though by far the worst, so I kicked him out of the group. I take such demands very poorly. The PC's background is not a contract on me in any way.
Yeah, well, there's always THAT sort of player.

I think we've all seen that sort of thing. And, since, as you said it wasn't the first time, giving him the toss is probably the best idea.
I've run across that as well.
A lot of this sort of thing can get nipped in the bud with sitting down with the players, before any character is created, and being extremely open about what your campaign is about and what you expect from it. Don't pussy foot around it and don't wait until you have problems to try to fix them.
Fear the Boot (a podcast I regularly listen to) calls it a Group Template. I think it's an absolutely fantastic idea. Instead of everyone going off to write up their characters, showing up on the first game day and trying to shoehorn things in, have a very detailed point form list of what your expectations are for the campaign and have everyone sit down and talk together about them.
Once you do this, and get everyone on the same wavelength, so many of these issues go away.
S'mon, I realize you have a problem doing this simply because of your gaming situation. My advice would be to have a short, one page handout of THE RULES. Since you're almost running a sort of Convention game where you have players coming and going constantly, you can't really afford the time to build up that level of trust between you and the players.
I know in my first OpenRPG campaign I had a similar issue. Actually, in a few of my campaigns I've had this issue. In my first camp, I had two players who always showed up, one that was very casual and two chairs at the table that changed almost every week, certainly every month. It was brutal. A completely eye opening experience that was. This was where I developed my The Rules guidelines and they got revisited and revised constantly for a while.
When I ran my World's Largest Dungeon campaign, my group had settled for the most part. I had four players that were pretty much rock solid and a fifth seat that seemed to get changed far too frequently. It became something of a group joke that anyone who sat in that seat was doomed to fade away to nothing. But, since I had a more static group, I could really start to build up the trust between the players and myself and relax my grip considerably. The players themselves began policing each other much more than I do.
Now, with my Savage Tide campaign, the group has been pretty much together for over a year now, with an addition of a sixth player a few months ago. Having a stable group makes a world of difference.
Thinking about it now, I think that's where our different approaches lie. I have a stable group that is all on the same channel as I am (more or less) and I know that they aren't going to pull red dragon crap on me.

You're in a different situation, where you are constantly gaming with strangers. Makes "say yes" much, MUCH more problematic.
I wonder what Gregk's situation is. If you're still reading this Gregk, do you have a fairly stable group or are you gaming with strangers often? On a side note (because I missed your post a while back) I agree that a player who refuses to compromise the background of a dragonborn would be a problem. If he's insisting that a dragonborn MUST come with the entire package listed in the PHB, then, yup, I 100% agree with you that I would likely say no as well because that entails too much change in my campaign world. My question to you is, what if the player is willing to change the flavour, so that it suits your campaign world (heck, using the tried and true "fell down a rabbit hole and is trying to get home" trope works), would you still veto dragonborn?