At the end of the movie Good Will Hunting, we see Will drive off to see his former girlfriend "...gone to see about a girl..."
Prior to this, Will had excepted a job, and stated his "...boss seemed nice..."
Will had been offered Govt jobs, and turned them down due to his belief that he would be doing the wrong thing and aiding in harming people rather than helping them.
What is Will Hunting went off to see his girl, but instead, without anyone to influence him (Doctors and friends) was taken by the Govt (who know how valuable he is) and turned into Jason Bourne.
Jason Bourne is David Webb. Who had a father and a mother.
What if, the David Webb persona, is actually a deep deep layer of his brain washing to turn him into Jason Bourne. Will Hunting has no real family. David Webb did - to give the persona a personal connecting to the project and to fill in missing parts of Will Huntings life.
Will Hunting becomes David Webb. Brain washing part 1.
David Webb becomes Jason Bourne and is training in all attributes of the kick-ass-ness that Bourne possesses.
Bourne is the best of the best. Super smart (he all ready had this as David Webb aka Will Hunting), and the rest was his training and the chemical program we know off.
Bourne doesn't trust easy. Neither did Will Hunting.
Bourne is a natural fighter. So was Will Hunting.
Bourne risked his life save people. Will Hunting would do that for his friends.
Bourne would make remarks to people he was hunting. Will did that "...how do you like them apples?..."
So, the David Webb character is a layer to hide the Will Hunting personality - to allow for Jason Bourne to be created. If the Bourne persona comes crashing down, it all falls to Webb persona - which can be rebuilt again by the Govt.