Some details about the Lenz vs Universal case and the video in question

In a recent case, Lenz vs Universal, the court had to decide "whether 17 U.S.C. § 512(c)(3)(A)(v) requires a copyright owner to consider the fair use doctrine in formulating a good faith belief that 'use of the material in the manner complained of is not authorized by the copyright owner, its agent, or the law.” Here are some details about the case:

Stephanie Lenz uploaded a video on YouTube of her children dancing to Prince's song "Lets' go crazy". Universal sent a DMCA notice to YouTube asking them to take down the video because it was violating copyright. Ms. Lenz claims that the notice was sent not because of any specific characteristics of the video in question, but "as a matter of principle" that Prince "has the right to have his music removed". Contrary to this principle, in the case of "fair use", copyright owners don't have the right to have their music removed.

So was the video "fair use"?
According to the Copyright Act, in determining "fair use" four factors should be considered: (1) the purpose and character of the use; (2) the nature of the copyrighted work; (3) the amount and substantiality of the portion used in relation to the whole work; (4) the effect of the use upon the market for the copyrighted work.
Here are some technical details about Ms. Lenz's video related to those factors:
(1) The video was intended for non-commercial personal use. It's just her children screaming and dancing to the song and has no real market value.
(3) The video is 29 seconds long, while the whole song is about 4 minutes (3:46). The music is playing in the background as Ms. Lenz is talking to her children. Due to the poor quality of the video and the interfering noises, the song is almost unrecognizable. According to the court, "The audible portion of the song includes the lyrics, "C'mon baby let's get nuts" and the song's distinctive guitar solo." We will have to take their word for that because it would be hard to actually recognize the lyrics from the video.
(4) Because of the reasons mentioned in (3), it is hard to believe that this video has the potential to influence the market for Prince's music in any way.

For these reasons, the video is obviously fair use, and that fact would have been obvious to whoever sent the DMCA notice. So the question is not whether or not this video constitutes fair use (because it obviously does) but rather whether Universal should have watched the video and considered the possibility that is was fair use before claiming that it was violating copyright. Universal claims that they were only required to do that after they received the counter-notice. According to the court decision, Universal were indeed required to consider the fair use doctrine before sending the notice. Whether they did that remains to be determined in court.