You can take in-game pictures in Brawl; they just won't be in a format you can use. If you use an SD card, you can take the pictures from there to your computer.
In order to make them usable, you can either download the .bin to jpg converter in the resources section and convert them yourself, or just send me the pictures and I'll convert them for you. This time.
But there's no reason not to convert them yourself.
Unless you're using Dolphin (some people do), in which case, can't you just use some kind of screen recorder?