Situation and skill

I found a post on Tales to Astound that talks about something that has been bugging me for a while now.
(OK, I apologise for taking it out of context a bit - the author is actually talking about impartial Refereeing. But I've got that part down, and am more interested in his intro...)

In older games (Classic Traveller, OD&D, according to the author of Tales to Astound), a roll of the dice answers the question "is your solution going to work, given the situation, with the situation including character skills".

When you move to skill-based systems with the skill roll being central (pretty much all other versions of Traveller, Runequest, GURPS...) the same question becomes "is your character skilled enough to deal with the situation".

I agree with the author that the differences are subtle, but potentially important. One of this approaches is all about the situation, the other is mostly about your skill, with the situation providing bonuses and penalties.

Are we giving too much "weight" to skills and attributes (and other "who the character is" bits on the character sheet)? When you pull someone's legs from under him, you don't need to roll Athletics to see the result. He falls. He might even manage to make a handstand, but keeping his balance is out of the question, unless you really had no idea how to do that move.
You can roll Athletics to see how bad the fall is...but if the other guy is manipulating your legs, it depends mostly on the other guy, and what the floor is covered with (admittedly, the "depends on the other guy" part could be subsumed in the dice of the Athletics roll...)
In short: are today's system trying to make it seem like more depends on factors we can control, and lessening the role of luck and the environment? (I'm honestly not sure).

Then again, there are enough situations where skill is the deciding factor. How do you model that?

Questions, questions. If you've got answers, tell me!

What I know is this: tonight, I played Call of Chthulhu 7e, and the game actually worked just fine based on the situation.
The evil sorcerer went down when my dilettante (no special skill with guns) just went next to him, while the anthropologist in the group was distracting him with a rapier cane. The evil sorcerer and his zombie were attacking the poor anthropologist.
Me: Tell me where I am at the beginning of next round (no battle mat).
Keeper: You're 4 meters from the sorcerer, and 9 meters from the anthropologist who's trying to free the sacrificial victim while the zombie is attacking him.
Me: I shoot the psycho mesmerist in the face at almost point-blank.
The Keeper gave me two bonus dice (new mechanic in CoC7e), with which my skill was enough to pull up the shot. All because I didn't shoot from a distance, but waited to close in.
Then I killed the zombie by toppling a pile of crates on it, and while it was pinned down, I shot it behind the ear. Until it stopped moving, which wasn't on the first shot.

It worked just fine. Granted, that's due to me making sure to improve my odds...but basically, an untrained character who would have Skill-0 in Traveller, pulled off winning the fight quickly and decisively - by acting while the enemy was being distracted, and using the environment.
To me, it made sense things would work like that. And they did, which was nice.
Was that a good balance between skill and situation? I don't know enough about guns to tell, but it seemed to be.