I was too. "Backstab" was the original term, I believe.
And it was absolutely an expression of skills. Importantly, it was the only class that had skills rather than powers. (Hide in Shadows vs. Turn Undead) No one else had skills. If anyone else wanted to do things it was a 1 in 6 chance*, better if there were extenuating circumstances. These skills were also watered down in successive editions. Climb Sheer Surfaces became Climb Walls. Anyone could climb walls; the character had to remove all metal armor, be unencumbered, and had a bonus to their d6 roll if they had a rope. Thieves could freeclimb even with their backpack and gear. The other skills were similarly advantaged in theme.
And, as you note, as the class system transitioned to adding an initial engine-wide skill system, powers were added to the classes to strengthen their niche and archetype. So, in D&D there is more than a simple skill package to typify a "thief". The powers available might be unique to PC thieves, and NPCs only have the skill package.
I think which is why I disagree with the concept of "skill-monkey", especially in a class-based system. The Thief isn't a jack-of-trades character. They are the class that is supposed to be the best at stealth in an urban environment. I extend that to being the class most adept at urban environments: moving through, finding people, establishing networks, knowing who owes whom, &c. What I found to be an excellent JoT character is the Akashic from The Diamond Throne that Monte Cook initially published (now owned by someone else). They are the "skill-monkey" people want.