In the first video, where she's winning the race against others doing butterfly, she's not wearing swim fins so far as I can tell.

Here's a question: how do swim fins work?

I mean, it seems obvious, but when I start to think about the forces at play, and draw vectors, etc, things actually get less clear. Anyone have an intuitive but rigorous answer?

(My question reminds me of the "how do we suck in spaghetti" question, which once again seems kinda dumb but then is frustrating when you start to break it down. http://www.straightdope.com/columns/read/1260/how-does-one-s... )

As a swimmer, I was much faster underwater with fins than above water, up to a distance where I needed to breathe more than once a lap (~ 100 yards).

No, I wouldn't be convinced. There's a big difference between the two kicks and being underwater is a lot more efficient.