From your sources:
A form of speech protected by the First Amendment as a "distorted imitation" of an original work for the purpose of commenting on it.
Also found in: Dictionary/thesaurus, Acronyms, Encyclopedia, Wikipedia.
See also: caricature, distortion, irony, parody, ridicule
Burton's Legal Thesaurus, 4E. Copyright © 2007 by William C. Burton. Used with permission of The McGraw-Hill Companies, Inc.
I would trust Black's over TFD, and a lawyer over either of us. Still, there's nothing at either of those URLs that appears counter to the work being parody or satire. The definition is even more broad than that of Webster's.
There's a legal blog post (which is not by me and is not case-specific legal advice by anyone) from Legal Process Outsourcing Services that has much more about the topic. The "Elements of Parody" is exceptionally clear and important here.