I think people tend to make things far too complicated sometimes.
It seems most likely that there are two powers in the world: The Dark Ones power (called the True Power by the Forsaken) and the Creator's Power (called the One Power by everybody.) Because the Dark One is the opposite of the creator, his power is the power of destruction, which makes it both extremely addictive (destruction is addictive, after all, even in the real world) and singular (destruction does not need help if you are powerful enough). Because it is the power of the Dark One, he gives it to only those whom he chooses, which is those who will forward his desires. Because most of the creatures in the world have nothing to do with the Dark One, most cannot sense it's use.
The True Power, on the other hand, is the power of creation. It is much more subtle than the True Power, just as creation is more subtle than destruction. It is divided into two parts which both fight and cooperate, and which correspond to male and female. The tension between the two, as well as their cooperation, create the future, just as the merging of male and female creates the future. Just like the True Power, it is only given away at the Creator's discretion. However, as creator he has left the world's future in the hands of his creations, and thus made it generally available based on genetics rather than behavior.
Rand cannot access the true power, and does not have the Saa. That idea is based off of a very stretched reading of a phenomenon that can easily be explained by other causes.
The link between Rand and Moridin, however, is clearly real and an unknown at this point.