Not correct. Rand learned this because of the dual wounds on his side that repelled eachother, he then used that knowledge to basically push tainted saidin against Shadar Logoth to force the taint out. That was a hypothesis shown to be true through experimentation.
I'm going to go out on a limb here and say the DO is not the source of all evil, and we have already been shown that with Shadar Logoth and Mashadar. They were also evil, but completely opposed to the evil from the DO, and without those opposing evils Rand would not have been able to cleanse...