Universal Music Group sent YouTube a takedown notice, citing the Digital Millenium Copyright Act. YouTube took it down. Six weeks later, the video was back up. Lenz had filed a counternotice, and she was being repped by those fine upstanding citizens, the Electronic Frontier Foundation. Their stance was simple -- in jumping the gun to take down the clip, Universal did not consider if Lenz had a Fair Use right to use the music in the clip. The EFF is basically using Lenz's case to test the scope and damages that can be claimed for wrongfully hitting people with DMCA takedowns. The DMCA is bad as it is, but the wording just encourages it to be abused.
The judge ruled that the EFF had a point. They have to prove damages were incurred (the crux of Universal's defense), but this is significant in that the ruling establishes that the DMCA can be abused and if you do abuse it, you should pay somehow.