I've seen this a lot. I guess it depends on what you mean by "unique." If it is in personality and role-play how does that differ from any other role-playing game where you can play them differently.
How does 1eAD&D let me make a Fighter that has some stealth and/or can climb, you know, sortof like a young Conan but weaker?
I think it depends if the DM is of the camp: each class has their own area of expertise, and since Thieves have these skills no other class can unless explicitly stated.
As opposed to a DM of the camp: yeah a Thief has special abilities but climbing or moving quitely is something any one can do, your just not as good at it as a Thief who can do these things in really, really hard situations.
I submiit I met many a DM of the first camp who shut down you even attempting to play the Fighter in anything but one mode.