http://madconfessionsofaman.files.wordpress.com/2011/05/douc...
Similarly, being introverted doesn't mean you have low social skills.
I don't know how you can say that.
The definition here: http://dictionary.reference.com/browse/introvert?s=t
implies low social skills.
Even when people discuss it here, they talk about wanting to be left alone, not going to parties because they aren't interested in socializing, and feeling "weak" after socializing for a short amount of time.
With all of this, I don't know how your social skills could ever be considered high.
Social skills are the ability to make conversation, to make people feel comfortable, to engage others, etc.
Extroversion is the desire to do those things.
Yes, they are clearly correlated, but by absolutely no means interchangeable. There are plenty of introverts who have perfectly decent social skills, and plenty of extroverts who have terrible social skills, because the desire for something is not the same as having a skill for it. For example, an adolescent extrovert may feel strong motivation to be outgoing, loud, talkative, and active, but that doesn't mean he will have good social skills and be polite.
The most common psychological definition of extrovert and introvert that we currently use was largely shaped by Carl Jung, and his definition involves far more than just sociability. However, sociability is the easiest application. What it really comes down to (as the link you provided points out) is a focus on the "external world" vs the "internal world", so I use the word "are" in those two definitions above very loosely.
It also has a definition used in psychology as well, which is something completely different, than the term used colloquially.