Social skills are absolutely skills. They're learnable, somewhat teachable, and definitely not fixed at birth. A diagnosis of Asperger's isn't a life-sentence of nerddom.
The difference is in how easily you can learn those skills. I had to painfully, laboriously, slowly observe people and pay close attention to acquire my social skills. Nothing came naturally - at times I was thinking "That's totally illogical. Why do people ask 'How are you?' when they don't care about the answer?" I'm told that most normal people pick this up by osmosis. Plop them in a social situation, and they'll have an intuitive feel of what to do.
For an analogy, it may be good to compare to another skill. As a kid, I always had an intuitive feel for math, such that I could rederive trig on the car ride to a math competition (nobody in our school had had it yet, since we were only 7-9th grade and competing in a high school league) or place in the top 10 on the geometry section of a big math competition despite never having had formal geometry instruction. I assume this is the same sort of intuitive knowledge that most people have of social situations. But since it's expected that people will find math hard and people easy, there's a whole institutional structure for instructing people in math. Similar support structures for instructing people in social skills are often stigmatized - why can't you figure it out on your own, people think.