At the Cleansing Osan'gar doesn't really seem to care if Rand lives or dies. The only reason he is there and tries to kill Rand is because he's afraid that Moridin or the DO will kill him if he tries to run away. I believe the only reason he attacked Rand at the end of PoD was that he believed that the overwhelming odds were in his favor to remove Rand as an obstacle. However, we know that the Forsaken are ordered not to kill Rand. Something that is obviously not passed down to the lower level DFs, like Slayer, or Taim. I just don't see Osan'gar having the motive to do it.

Aran'gar has no connection to the Asha'man who we know found Rand's inn and therefore has no real way of knowing where Rand is.

Taim on the other hand is apparently a high ranking DF and likely has gotten a lot more influence in their circles due to bringing in such a large number of new Dreadlords. It's not beyond reason to assume that the DO might have granted Taim some of the same privileges he granted the Forsaken, like immunity to the taint and access to Slayer. Also, Slayer's patron exits into a snow covered forest, which is very similar to the area around the Black Tower.



I have read all the parts with Slayer, there's nothing to indicate that he can take anyone face to face, give me a quote from the books that even remotely points to this. He gets the drop on Perrin twice and fails to kill him, the first time he runs away and tries to get Perrin to enter the ToG, the second Perrin turns his own game on him and almost kills him. The only confirmed kills he has are two bound AS, two old people sleeping and a grey man, possibly the one Nynaveve wrapped in Air back in tGH.

I doubt that Asmo was more surprised by whoever killed him then Rand was in LoC when Bashere throws a knife at him. If Asmo hadn't known who Slayer was, then maybe that'd be enough, but upon seeing Slayer he should have known that he'd need to defend himself. Slayer on the other hand would have no way of knowing that Asmo would be coming through that door at just that moment and would therefore likely be just as surprised.