I'll have to go dig up the original MP3 recordings (I can't download from the computer) and see, but if I recall correctly, I think that it's fingerpicking throughout except for the final MP3, which is on the twelve string. I believe (and I think the MP3 says so) that I used a pick on that one. But I could very well be wrong.
As to how one should learn the lesson, either way is fine. When I perform this in public, my decision to use a pick or fingerpick is usually determined by matters that don't have anything to do with the song (or any song, for that matter). Things like the sound system, the place in which I'm playing, which guitar I have, the mood I'm in, how much my fingers hurt...
So personally (obviously!

) I think that it's important to be able to play
any song you know in many different ways, simply because you never know in what circumstances you might want to play it.
But, as I said, that's just me...
I'll let you know for certain when I dig up the files...
Peace