Of course the same reasoning applies to anything the Shadow sent to kill Rand, Slayer or Grey Man.

I've long been convinced Siuan had it wrong. She was the target, not Rand. She moved, the arrow missed.

And yes, the assassin might have been Slayer, someone good anyway. The BA had it set up nicely when you think about it. Half the Hall had sough to prevent Siuan from going to Fal Dara. The Amyrlin isn't supposed to put herself in danger, and now she went and got herself killed. Elaida had already presented her case to the Hall, even the Green Ajah (BA Sitters) tried to oppose Siuan.

It makes even more sense now Verin's been revealed as BA. There's only so many things she could hide from Alviarin who was present at Fal Dara, not to mention from Ishamael himself. She secluded herself with Siuan and Moiraine, questions would have been asked about their plans.

Siuan assassinated, without suspicion being attracted to the Black Ajah and it seemed to be an attempt on Rand himself.

This was an early attempt to get rid of an Amyrlin with too clever plans and secrets, and this was followed up by an attempt on Moiraine's life, the other side of that meddling duo. The attempt on Siuan's life failed, the opportunity had passed not to attaxt attention on the Shadow wanting the Amyrlin dead, it had to wait for Mesaana's better plan to remove her many months later, which worked. In the meantime, the Shadow spied on Moiraine and Siuan.

I suspect Verin knew all this and it played a part in her decision to leave Siuan and Moiraine. It's wouldn't be the only time Verin decided to scamper after failed attempts by the Shadow. She vanished after the Fal Dara events, she made sure not to go with Rand to Falme, she left Siuan's side to go in the Two Rivers with Alanna, she left Perrin right after his battle with Isam's army, she stayed well away from Rand in Cairhien, preferring to stay with the WO unlike other sworn AS. And she left Rand's side right after Rand's conversation with Logain about Taim. Verin never liked too much remaining around important people too long, as if she feared orders would come to do something drastic she could not evade or feared she'd be forced to give her superiors too many secrets.