As said above, naturally leaders have a better insight in the structure of the Shadow and more freedom to act as they want (Galina even says that she could tell the name of any person and this person would die). Therefore it simply makes sense - after infiltrating the BA in general - to infiltrate the Surpreme Council as well and thus learn their plans. Since Verin would even want to capture a Forsaken, she certainly didn't hesitate to climb in the hierachy of the Shadow to get more informations.

Plus, that Mesaana visited Verin twice shows that she is not an insignificant random BA, but a leader. This also explains Sheriam's quote very well.