DMCA violation over Prince Video?

As I mentioned in my previous post about my friend Rachel, the DMCA can be applied in totally insane ways. Here, it's being applied by a company that actually does have rights to the material claimed to be infringed upon, however the "infringement" amounts to fair use of the material.

The lady, who has a toddler son, videotaped him dancing to a Prince song, presumably when it was on the radio. The video is only 29 seconds long, and there is clearly no ill-will or malicious intent on the part of the mother, but UMG has decided that they need to take action to "protect" their property.

Now the EFF is filing suit (full complaint) against UMG, claiming that the invocation is frivoulus. I really hope the EFF prevails.