Remix cases have gone through before with a successful fair use defense. The issue is primarily relating to the amount of original content used. If you do a mostly original song, but mix in a particular word or phrase from licensed music, it could well be considered fair use due to the low amount of content used. If you're just laying dubstep over top of the original song, that would be much less likely to be successful.
Fair use isn't a set of strict rules that are easy to determine and it doesn't apply to private platforms. It is a legal defense in the case where you get sued by the content owner.