Rather than let his Super Soldier project die a funding-less death, General Ross decides to reach out to a weapons company that has a very personal history with Project Rebirth. If Tony Stark had been more involved in the nitty-gritty of his company, he'd have rejected the proposal out of father-related spite. I guess it's a good thing Obadiah Stane runs the show.

With the research now able to continue, there's certainly no reason for Dr. Bruce Banner to hastily (arrogantly) inject himself.

[Timeline note: Banner's Hulkification took place in 2005. Tony became Iron Man in 2010.]

I don't mind Bruce/Betty or Tony/whoever, but please allow those relationships be temporary and Bruce/Tony be end-game.