Parodies are a sensitive subject. Take a look at this case I found when I was doing my Business Law class a few weeks ago:
http://www.songrights.com/infringe.htm
This is also what my law book said:
"A copyright holder’s right in a work is not absolute. The law permits certain
limited unauthorized use of copyrighted materials under the
fair use doctrine.
The following uses are protected under this doctrine: (1) quotation of the copyrighted
work for review or criticism or in a scholarly or technical work, (2) use
in a parody or satire, (3) brief quotation in a news report, (4) reproduction by a
teacher or student of a small part of the work to illustrate a lesson, (5) incidental
reproduction of a work in a newsreel or broadcast of an event being reported, and
(6) reproduction of a work in a legislative or judicial proceeding. The copyright
holder cannot recover for copyright infringement where fair use is found." (Cheeseman, 2013).
Also, look up the recent Beastie Boys copyright case. I guess people can disallow fair use of their work if they want, this is new news to me.