Fair Use

Came across this today. With all the conversations about piracy and what not, I was surprise to see what actual US Copyright law looks like, particularly the definition of Fair Use:

the fair use of a copyrighted work, including such use by reproduction in copies or phonorecords or by any other means specified by that section, for purposes such as criticism, comment, news reporting, teaching (including multiple copies for classroom use), scholarship, or research, is not an infringement of copyright.

My school district has very strict guidelines for films that can be shown in class, largely because of copyright laws. Does this mean it would be legal for me to download a pirated video for use in my classroom? Just wondering...