An interesting question. I think QB is probably the most situation independent position ( assuming that the QB you're talking about is the starter, and not someone like Mallet who's stuck behind a stud. then it becomes the most situation Dependant). There are things that can make a qb more desirable, and some qb's skill sets don't match coaching styles, but if you're a truly great qb, you can produce numbers no matter whom you're throwing to ( see Peyton Manning over the years).
Historically, I would have argued that running back is the most situation independent position, that elite stud running backs can excel on bad teams and bad offenses ( SJax being a shining example of that). However, with the emergence of RBBC, RB is becoming more and more situation Dependant. Studs like Jstew and DeAngelo cannibalizing each others numbers, guys like Charles wasting away behind less talented starters, teams taking stud rbs like Best and Leshoure in successive years in the draft. As the use of running backs become more and more specialized, I think situation will become more and more important.
However, I think the most situation Dependant position are the receiving positions, WR and even more so TE. Receivers are completely dependent on QBs to get them the ball. A bad QB can wither your production. Sure, some studs like LFitz can still put up good numbers, but when he had a HOF quarterback, he was a top 2 receiver. If you have a dynamic passing offense, numbers can be inflated. There has only been one receiver I've ever seen, who I thought boosted his QB's value and not vice versa, and that was Randy Moss at his peak. Most WR production is extremely dependent on system and QB. This becomes even more exaggerated with slot type receivers, who depend on chemistry and timing with a QB over sheer physical dominance. I think this is even more the case with TE's When a guy like Tamme can step in and match Clark's (a top 3 fantasy TE) production, I question how much Clark's talent matters. Sure a guy like Gates would be productive anywhere, but how much has having Rivers throw to him boosted his value? With one QB, Celek was a top 5 TE, with another TE he's forced to block more and is rendered useless. Some systems and schemes don't feature TE's as receivers at all, like Mike Martz's offense. Would Greg Olsen be a pro bowler if he was on Indy?
I think what system a receiver or TE is in, is a very valid consideration when you're making a trade for a veteran player, with the idea that you want to win now. In drafting players, or trading for a young players, I think you can almost disregard situations though, because situations change every year, but talent does not.