Someone commented somewhere above that there is no reason for Nick Fury to show up in IM2 -- to give Tony a medical stop-gap measure or anything else -- 
without the Avengers connection... but I don't think that's true.
Let's go back for a moment to the idea that "in the Marvel universe, SHIELD = a gov't group like the FBI or CIA or ATF or Secret Service, but one specifically dealing with super-powered beings and weird crap".  I assume this is a basically fair summation of what SHIELD is supposed to be.  
If this is true, then 
nevermind about The Avengers Initiative.  Forget about it for a moment.
Tony Stark, in IM, made himself into a super-powered being (albeit mechanically).  The moment he did that, he became someone SHIELD would need to monitor and know about.  They are the government.  They at least want to keep an eye on all the vigilantes and individual operators.  
That's why Fury shows up at the end of IM -- he says it specifically  ("think you're the only super hero in the world?").  Tony has just outed himself as a super-hero.  SHIELD's eye is now going to be on him.
The Avengers Initiative is an additional function of SHIELD, and it's apparent in the conversation in IM2 that SHIELD is evaluating Tony to see whether he can or should be included in The Avengers.  Because Tony is that much of a person of interest to SHIELD, that's why SHIELD is already prepared to help Tony with his medical problem. (Of course, in the end they decide "no", they don't want him as more than a consultant in their project, as he's too much of a loose cannon).  But, even if Iron Man never becomes an Avenger... SHIELD will still be keeping an eye on him.  Because that's what they do.  Just like it's the FBI's job to keep an eye on who the big players are in the organized crime world.
It is no stranger, within the world of the Marvel universe, to have the head of SHIELD talking to a super-hero, than it is in a movie about the Mob to have an FBI agent talking to a mob boss.
	
		
	
	
		
		
			Next thing you know people are going to say Thor fans who don't see the Avengers are screwed because Thor will find his way back and forth from Earth and Asgard in The Avengers.......This is like saying "so and so won't understand The Return Of The King because he never saw The Two Towers"...tough luck.  Marvel even added the "_____ will return in The Avengers" lines at the end of the last few films. Avengers is basically a sequel to each film. If someone misses a part of a film series, its their responsibility to catch up,not the script writer's to baby step them into anything. Plus I don't know a single person who didn't like at least two of the Avengers properties, unless they liked zero of them.
		
		
	 
Right.  It's also like saying that you're annoyed that you can't watch Harry Potter 7, because you didn't see 5 and 6.
And I guess I can see why some folks are annoyed at that idea, if they didn't think they were signing up for a connected movie series when they first sat down to watch Iron Man.
What I still don't really understand is the view I've heard some express here, which is something along the lines of, "If I'm just a fan of Iron Man or Hulk, then I don't want allusions to other heroes or entities in the MCU to intrude upon their stories".  
The reason I don't understand this I suppose is that even as a comics reader, as a follower of certain characters... I've never been the type of reader who, say, only wanted to read Aquaman's solo books, but wanted to ignore his presence in JLA books if he was on the team at the time.  If I'm a fan of the character, I want both.  More to the point, if I'm a fan of the character, then I recognize that both things are important to the overall make-up of the character. 
So I can sort of understand if you are a fan of Iron Man, but you aren't particularly a fan of Thor or Hulk.  But I don't get how you can be a fan of Iron Man and not fold into your understanding/appreciation of the character the idea that he is an Avenger.  Maybe you never pick up a Thor or Hulk solo book, but do you really ignore all of Iron Man's presence in Avengers stories?  Do you really never want to read The Avengers at all, even when he's on the team?
If so... okay.  But it's not something I'll ever understand about someone else's reading habits.   And at the same time, I don't understand how someone could not realize that for many comics readers, there is intense enjoyment to reading all of a favorite character's appearance in various titles; or to seeing reference in the character's own title to the fact that he exists within a connected world.
I mean, I've said before -- I'm not a fan of the Hulk.  Therefore, I didn't go to see either of the Hulk films in the theater.  But I don't get the idea of being pissed off that I had to go out and rent the Hulk (for $1 from my library) so I could watch it and feel like I wasn't missing anything in preparation for The Avengers.  It wasn't a terrible movie (actually I thought it was quite good), and it didn't feel like a chore.  
Is that what it sometimes comes down to, though?  Are people annoyed because they feel like this connected series of movies is "forcing" them to be conversant in the other entries in the series?