I still find far more likely she's referring to information she got from her own BA. Moghedien in book 4 showed a disctinct lack of knowledge and interest in what didn't concern her little domain in the south. She didn't even know Rand's name.

Beside, as we know Moghedien is still running those BA. She had no need to go to the Tower to get Alviarin to tell her what one of her own pet BA could tell her. Notice she doesn't even wonder if Hessalam could be Sharina. She simply has no idea Sharina exists. She must have thought an instant Hessalam was BA - perhaps even that she was their leader or something.

I don't think the new scene tells us much about strength, but I get the feeling Moghedien was probably always underestimated because of her personality.

I don't think she's much weaker than the others, probably just by something like the difference between book 4 Nynaeve and Nynaeve at full potential. I think Nynaeve at full potential is probably in the range of the levels on which Graendal, Semiraghe, Mesaana stand. She could be on a level lower for instance, or at the lower threshold of the same level, or their equal more or less. I get the feeling all those women are distributed on few levels, a few below Lanfear.

It could be significant, but in that range it's far more the combination of knowledge, training, experience, Talents and skills that would set these women apart than raw strength, and in combat it's only if they find themselves in a head-to-head confrontation strength could be a determining factor. I think only Lanfear/Cyndane has a clear raw strength advantage over the other women - which is useful only in some situtations, and even then they're all strong enough they'd probably dare attack her if they had a plan they believe would neutralize her strength advantage.. Graendal did... with a small angreal and her most potent weave she took Moghedien and Cyndane face on, both at once.

Moghedien simply overcame most of her complex of inferiority since the Cleansing. The fact she was in disgrace and humilitated still made her feel inferior to the others, but now that Graendal's joined the club Moghedien realized Graendal no longer intimidates her at all and she dared laughed at her openly. What the scene tells us about their respective strengths is more or less only that Moghedien's not weaker nearly enough to stop her from provoking Graendal. It was more a matter of complex of inferiority and lack of self-confidence that made her stood aside to an extent, made her avoid being openly challenging because she feared confronting them openly. Not anymore, not for Graendal anyway. She already seemed not to fear Cyndane much.