Isn't fan subbed anime technically a derivative work and therefore protected under fair use?

i.e. It's legal to take licensed work and make a parody and distribute as long you're not making money off of it.

I watched the Naruto fansub from funimation last week, and a lot of the subs were inaccurate, and could be construed as a parody, so technically should be legal even if someone licenses it. Now a derivative work needn't be a parody.

Anyways, just wondering about the finer points of the copyright law.