I don't think I defined what I think 'skill' is. First let me separate a common omen. Pretty much every shooter you play this day is highly defined in team play: you aren't going to win in 1vs4 situations in any shooter these days but a person's level of individual skill is about the mastery of mechanics.
First instance, take Gears of War. It's a cover based shooter. On a low level that's all it is: you sit behind a wall and shoot stuff. To a highly skilled player they know how to use cover as a movement tool and can move around it much more quickly
virtually wall bouncing around you indefinitely. On the surface of it, an average player may not even think to 'wall bounce' but it's an invaluable tool in mastering the cover system. This is before all the shooting aspect of it. There's no tool or game system in Battlefield that's about positioning and out maneuvering. Ok you can duck behind cover or go prone in the trees what other tools are there that allows you to out position a player in 1v1 battles or just even getting out of bad situations?
Which leads me to my next point, the shooting aspect of 'modern warfare' games is a see first, die first, dice roll - as I mentioned. I get the appeal of "realism" it invokes but I don't think a virtual luck of the dice is about skill. Unless you know where all the camping spots are, you aren't going to 'see' first 100% of the time. Hell, not even 50%. In Halo, even if you catch me out in the open the game's system gives me to the tools to get out of any situation, it's the same in Gears. What are you do when you roll that dice some player simply gets the drop on you?
You talk about team play, there's far more it in Gears than any modern warfare shooter I played. If you think you're badass, the lone-wolf, you are going to get blown up. I can't count how many times in Battlefield 3 I've had a K/D of 7, 8 or 9 just lone-wolfing it. Since Gears is so individually skilled based 2 people of my skill level on the opposing team, coordinating, with me lone-wolfing it gets me blown up about 50% of the time. That's a K/D of 1. That's a 6-8 point difference. Which would turn a match in Gears.
....anyway I'm rambling again but hope you get what I mean about "skill".