Express Yourself vs. Born This Way

(Re)mix of Express Yourself by Madonna and Born This Way by Lady Gaga.

When I tried to upload this mix on Soundcloud, it wouldn't let me do it. I was redirected to a page with an error message reading "This track contains protected material that is owned or licensed by Warner Bros., Inc." Then there is an option for feedback, so I wrote a little rant about how I think this should fall under the category of fair use. Since the remix is not an exact copy of the original work, and in fact creates new value and meaning as a remix, it should not fall under such stringent copyright law. Moreover, I am simply sharing the mix with friends and not making any money off of it. (I declined to monetize this track on Soundcloud by linking it to Beatport or iTunes.) To me, this is a clear example of work that should be protected by fair use.