Why doesn't it say that Graendal "killed" Asmodean, if she actually wasn't just "responsible" (also SH used the word "responsible", not that Graendal killed Asmo). It makes sense, though, if a "tool" of Graendal killed Asmo, namely Slayer (perhaps as Luc, who knows the Caemlyn Palace of course).

Graendal doesn't think and Moridin doesn't mention that she used Slayer before, but it's also not mentioned that she didn't. In the same way, one should wonder then, why Graendal doesn't think -or Moridin mention - that she directly killed Asmo, if she did it.