I have curly/wavy hair that gets frizzy and fuzzy and behaves much like Jason's does (though it's a different shade - a red that has hairdressers asking me every time, "Is this natural?"). I don't do much with it beyond a good shampoo, a brush, and a ponytail (especially for skating). But on competition day, I'll break out the straightener. It's all very well to know that curly/wavy hair looks nice, but when you need it under control to an extreme level, the straightening iron is your friend.
I think Jason does straighten his hair for comps, but I think he mostly does the top part, which is the bit you really need to get under control. I remember him mentioning a few years ago that it took him 20 minutes to straighten his hair. It's quite possible to straighten hair but leave curls at the end.