This treatment of others as one wishes to be treated is an inherently non-discriminatory and universal ethic. There is no remaining trace of the divided ethical view that the argument against Ethical Egoism attacked because each individual is treated by every other individual in a comparable way, due to a selfish desire to have all others treat one equally well.
In the other case, that of Natural Law, the primary argument made for the invalidity of the theory is that there is no appropriate value claim argument made to support the logical leap from 'is' attributes of the universe to 'ought' attributes of human society. There is no reason that we should follow the morality indicated by the natural laws of the universe. However, this argument too can be countered by an application of the principle of one theory to the other. In Natural Law Theory, the natural laws of the universe derive from a universal law dictated by God. Now, if accepts this premise of Natural Law theory as stated, then one accepts the existence of God implicitly. Now the universe, which according to this premise was created by God, appears to work relatively well- as evidenced by the possibilities of Unified Field Theory, and the fact that there is no apparent contradiction in any of the hard sciences in the way things work- scientific laws don't have exceptions to prove the rule as do others. It would then seem reasonable to assume that if the world works by God's universal law in a good manner, then an individual life ordered by precepts derived from such laws would have similar value. Then, if one applies the Ethical Egoist view that an individual should do what coincides with that individual's best long term interests, and to follow the moral codes derived from the universal law would result in a good life, then one should most certainly follow those precepts, thereby providing the needed value claim to bridge 'is' and 'ought'.
It would seem that although based on wildly different premises, a case can be made that Ethical Egoism and Natural Law theory can complement each other to a limited degree, indicating that perhaps there might be a closer approximation of moral truth found by looking in the middle somewhere.