I don't agree with Fionwe, I think that Brandon answered the question in totality.

This debate has originated from the fact that no one believes that SH can detect a weave of saidar on Elza. I don't agree with this. We've seen years ago that Myrddraal can detect even the smallest thread of Earth channeled by Egwene, and SH is a super-fade with vast powers but also vast limitations. Verin also used an angreal to weave the Compulsion so she buried a great deal of saidar in Elza. Not only that, but I believe SH to be a direct part of the Dark One in a Fade's body, and he could have deduced from Elza's behaviour that she was Compelled. He may have ordered her to kill Rand, and seen her struggle to obey despite terrifying her.

Either way, there are far too many flaws in this Graendal theory. He would never have needed one of the lowly Black Ajah to help him if he had Graendal with him. Going to all the trouble of teaching Elza rare weaves would be useless in the presence of a female Forsaken. It's also flawed to think that Graendal is the most logical choice here just because Compulsion is present in the scene. Obviously Cyndane and Moghedien are the most logical choices, being the tame servants of the Nae'blis. Either would do exactly what Moridin or SH wanted, whereas Graendal would not necessarily - she proved that in the Prologue. It's her instinct to toy with Moridin. Furthermore, why would this female Forsaken tell SH who would tell Elza? She'd obviously instruct her directly.