So a fair conclusion to draw from this would be that a possible difference between "old" and "new" school gaming is that one favors the player's skill and the other the character's skill?
When this thread first appeared a few days back, I wrote a very long post (even by my standards) addressing this topic. It got eaten by a server error, and due to a distraction (in the form of a 4 year old girl) I didn't notice until the text was unrecoverable (even through fiddler). I guess I'm going to have to try to rewrite it, because no one here is quite representing my opinion.
But, before I do that, I'll make a very brief answer to your question.
The short answer to the above is, "Yes." The longer answer is that neither 'old school' nor 'new school' is inherently entirely one or the other and that, while it is possible to play it entirely one way or the other, in practice most people don't and have good reasons for doing so.
I have always played, even since the early 80's, something of a hybrid game where player skill supplemented character skill and vice a versa.
Consider a 1e character skill like 'Find Traps'. This was never the only way to find a pit trap. You could do all sorts of creative things to spring a pit trap: the classic probe ahead with a 10' pole, fill a large sack with dirt and have someone burly repeatedly toss it ahead of you as you went down the corridor, summon some suitably heavy monsters and send them down the corridor to break a path for you, or drink a potion of flying and gingerly put your weight on the floor until you sprung the pit open. In 1e, in the role of a thief, at one time or the other I've done all of these things. However, in most cases the first thing I did was roll to 'Find Traps'. The way I was taught to play, the 'Find Traps' roll was made by the DM - not the player 0 and was made in secret. In this way, the player never knew whether, if he didn't find a trap, it was because there was no trap or if it was because his character wasn't observant enough.
If I had to point to one thing that is different about how I run the game and the way most players learn to play 3E, it's that.
You see, if I told the DM I was searching the floor for traps, and the DM said, "You find a pressure plate.", then I had something to work with and so much the better. But, if he said, "You don't find anything.", I didn't know what that meant and so I then resorted to my backup plan, generally speaking a 10' pole. Finding the pressure plate with my 'Find Traps' roll was far far better than finding it with my 10' pole, because that meant that I could avoid the trap which is far far better than springing the trap, even from 10' away. Being 10' back was sometimes good, but sometimes it was of little help.
So there was an intersection between player skill and character skill in I think a very interesting way. As your character got more experienced, his character skill got better and that helped you make better decisions, but you still had to fall back on your basic player based problem solving in many cases.
I think by pretending that the dichotomy is so huge, people are doing themselves a disservice by pretending that the two approaches have no problems (or rather by pretending that
their favored approach has no problems and that the other approach is just all wrong). I've seen bad DMing in every edition. There are pitfalls to avoid in both a player centered game and a character centered game. The best games tend to do some of both. I mean really, where were these old school games where noone rolled to detect secret doors or find traps or for surprise or any of the other proto-skill mechanics? I'm sure there were some out there, possibly games tied to oD&D, but even in 1980 I don't think that was how most people played. Most people were hybridizing their games, and the trick to playing 3e in a 1e style is achieving that approximate mixture again. In my opinion, the 3e rules set adapted to the 1e game makes for better old school gaming than any older edition does. I see no reason to go back to an old rules set that I abandoned in frustration in order to play in the way that I've always played.