I've heard this story many times over the years and was always found it amusing but was skeptical that it did HST any good. I mean, what use is it to blindly just copy something letter by letter?
I did Nanowrimo on a whim this year and it was a lot of fun (I doubt I'm actually any good at it, though). In doing it I found myself going to Gatsby and a Hemingway book (The Sun Also Rises) for examples of clear, direct prose. I thought back to this Thompson anecdote and thought to myself that if I ever wanted to really pursue writing, a straight copy of one of those books would help my prose ten fold.
So I agree with this article. Type out the code you're borrowing from, don't copy and paste. Also, tchlock23 is right in that you also need to start some small projects from scratch and suffer through them with minimal help.