Given that remixing potentially falls under the "transformative" portion of fair use copyright exemptions, this doesn't seem like it's set in stone, legally.
Of course, I imagine that most artists work out contracts with the copyright owners and simply pay the royalties simply because it's less expensive than a protracted copyright lawsuit. This doesn't make it a legal standard, however.
The US and many other countries have laws establishing the idea of a "compulsory license", which is (legally) required any time you cover someone else's song: http://en.wikipedia.org/wiki/Compulsory_license
Of course, I imagine that most artists work out contracts with the copyright owners and simply pay the royalties simply because it's less expensive than a protracted copyright lawsuit. This doesn't make it a legal standard, however.