I didn't see the video, so take this comment with a mound of salt.
Within copyright law under the fair use doctrine, yes Parody is protected. I use a capital P because Parody has a very specific meaning in this context. It doesn't mean funny, jokes, humour or any such broad terms which can be achieved or used subjectively. Parody very specifically refers to content wherein the use of copyrighted material in a piece of ridiculing commentary is essential. Satire on the other hand is a piece of ridiculing content where specific copyrighted material use is not essential.
So, my example is a common one as it is a real court case. There was a fair use attempt by a company to produce a piece of content to make fun of OJ Simpson through the use of the exact style and manner of Dr. Suess. It was determined by the court that in order to "make fun" of OJ Simpson, there was no need or justification of applying Cat In The Hat style verbiage and as a result it was ruled Satire, not Parody and thus not protected.
Far too many people believe that the simple act of creating a piece of content that ridicules something gives them total protection against copyright claims of all kinds and frankly this couldn't be further from the truth.
Now, to put a proper Parody use into context. If you were to use the same Dr. Suess style to alter the lyrics and make fun of a Dr. Suess book or the style in general, then that would be Parody under Fair Use doctrine in copyright law. This is because you can safely argue that in order to make fun of Dr. Suess, your project needed to use Dr. Suess material. It's also why Weird Al Yankovic often doesn't need to ask permission for material he makes which ridicules musicians (even though he always asks anyways).
