If I remember correctly the right to create derivative works is one of the five rights that can be licensed under copyright law.
IANAL but I would say if Coulton has a license from Harry Fox Agency to create derivative works, and the license terms allow him to retain ownership of such derivative works, then Fox may be infringing on Coulton's copyright. No?
If Coulton had rights to create a derivative, he'd be getting legal advice that he has a great (legal) case against Fox, if he's willing to spend the money and time. Though it isn't likely to make anyone fantastically wealthy.
If Coulton had a compulsory mechanical license to the original work, and just happened to create a unique arrangement and inadvertently created the derivative (he's no lawyer; how would he know a cover is only a cover until it isn't?) he'd be getting advice to let it blow over, because any action he happened to win against Fox on the grounds of their infringing his derivative would leave him open to suit from the original rights holder for not having had a license to actually create a derivative.
As Coulton termed the advice he received as "I have no case" I'm guessing he's not put off by the practical concern of time/money but by bad legal prospects. Particularly considering he went on to mention that he's still looking into whether they actually mixed in his original audio. (which, if they did, he could use to bring a copyright action against them without claiming that he created a derivative work.)
IANAL but I would say if Coulton has a license from Harry Fox Agency to create derivative works, and the license terms allow him to retain ownership of such derivative works, then Fox may be infringing on Coulton's copyright. No?