Also agree! For the longest time I mistook being socially crippled/anxious with being introverted. While I am indeed a quiet person by nature, being a quiet person doesn't mean you should have a hard time conversing with people, a hard time looking them in the eye, a hard time even approaching someone for a conversation. It should only change how you approach meeting and interacting with people. I'm worried that many people like to think their "introvertedness" is fine and good and a perfect excuse to sit in your house all day and not interact with anyone. As soon as I recognized this, I've been able to restructure how I approach and make new friends/acquaintances. Small social gatherings, clubs that promote meeting others through passionate interests that everyone has, etc. etc. Your third paragraph is spot on, ref.
I think being able to tell the difference between social anxiety or ineptness and introversion is pretty important. I've never had a hard time doing any of these things you describe as being central to social skill; I just get worn out more easily from it than others.