There's nothing in the movie that suggests the origin of the nickname can't come from both McCoy's comment about his ex-wife and the old term "sawbones". Maybe Kirk remembered McCoy's comment and decided that "Bones" would be a doubly appropriate nickname since he happens to be a doctor.
I really think you can have it both ways here.
It just strikes me as a really silly way to get a nickname.
"Hey, my mother just died and all I got from the inheretance were her bones!"
"I'm going to call you Bones!"
Makes as much sense.
Why give someone a nickname off a flippant, quick, comment they made over a painful situation that forced them into a whole new life?
But I guess it "more bothers me" that many are saying "OMG!!! We finally know why Kirk calls him Bones!!!"
Which makes me roll my eyes and say: "We ALREADY KNEW!"
It just strikes me as silly.
Given how much McCoy was rambling Kirk could've just as easily have nick'd him "Blood Boiler", "Flask", "Scruff." Why pick one flippant, quick, word out of a whole conversation?
I will say, though, that I loved the scene and it instantly sold me on Urban as McCoy.
i'm gonna go with what was said onscreen in the movie, unless they tell me differently in a future movie
Then show me where on screen it's said that Kirk comes up with that nickname based on this one, quick, rambling rant of a conversation?
I *might* give it to you if after McCoy said it Kirk said, "Well, Bones, it's nice to meet you. I'm Jim Kirk."
But that doesn't happen. Therefore, there's nothing in this conversation that tells us *for sure* that this is how McCoy got the nickname.

So my theory (backed by the guy who created the character in the first place) is just as valid (if not a bit more so.) Since you're infering on a throw-away line that was probably more of a wink to the knowing audience than it was to be a genesis of a nickname.