Edmund's greed favors natural law over man's law because natural law doesn't care that Edmund is illegitimate. He claims nature as his ally because he is a "natural" offspring, and because man's law neglects to recognize his rights of inheritance. But, nature only serves Edmund as a convenient excuse for his actions. His actions against his brother and father are more a facet of greed than any reliance on natural law.
One might argue that Gloucester's cavalier attitude toward Edmund's conception mitigates Edmund's actions. When combining this possibility with Edmund's final scene, in which he tries to save Cordelia and Lear, Edmund clearly shows himself to be of different fabric than Goneril, Regan, and Cornwall. In many ways, Gloucester is responsible for what Edmund becomes. Edmund is as much Gloucester's son as is Edgar. In embracing the man-made laws that reject Edmund's legal rights, Gloucester is denying natural laws that would make Edmund and Edgar equal.
Gloucester also acts against nature in rejecting Edgar without sufficient proof of his wrongdoing; thus Gloucester shares responsibility for the actions that follow, just as Lear's love test results in his rejection of Cordelia. Both men are easily fooled and consequently, they both reject natural law and their children. Both act without deliberation, with hasty responses that ultimately betray their descendants.
