First, there's a step missing: parody does not "therefore" allow you to copy protected works. You have to determine whether this is "fair use", where you get in the neighborhood of parody in identifying "purposes such as criticism, comment, news reporting, teaching ..., scholarship, or research". Therefore you have to go through the balancing act that is fair use analysis.
In Campbell v. Acuff-Rose Music, Inc., SCOTUS considered parody as a form of criticism or comment, noting that "This Court has only once before even considered whether parody may be fair use, and that time issued no opinion because of the Court's equal division". For that case, the court continues
Suffice it to say now that parody has an obvious claim to
transformative value, as Acuff Rose itself does not deny. Like less
ostensibly humorous forms of criticism, it can provide social benefit,
by shedding light on an earlier work, and, in the process, creating a
new one. We thus line up with the courts that have held that parody,
like other comment or criticism, may claim fair use under ยง 107.
The important step in this ruling is tha
For the purposes of copyright law, the nub of the definitions, and the
heart of any parodist's claim to quote from existing material, is the
use of some elements of a prior author's composition to create a new
one that, at least in part, comments on that author's works.
If, on the contrary, the commentary has no critical bearing on the
substance or style of the original composition, which the alleged
infringer merely uses to get attention or to avoid the drudgery in
working up something fresh, the claim to fairness in borrowing from
another's work diminishes accordingly (if it does not vanish), and
other factors, like the extent of its commerciality, loom larger.
In other words, you can't catch a free ride on "parody" to reach a fair use judgment. Even if it were parody, "parody may or may not be fair use", as the court said.
That does not preclude establishing that the work in some other way comments or criticizes. Get a lawyer before you go doing this, in case you end up involuntarily making new law.
