But some members of the Supreme Council might know each other.

Even so, it's clear that Verin must have been on the Supreme Council for the other reasons I mentioned. Plus, it simply makes sense for a person who thinks that capturing a Forsaken would prove useful, that she would risk to infiltrate the top of the BA. After all, you naturally get more insight in the workings of the Shadow as a leader and certainly have more freedom to do what you want.

Besides that, we also know that Mesaana visited Verin twice. Obviously Mesaana also visted two other leaders, namely Alviarin and Sheriam. It makes sense that Alviarin gave Mesaana at least the names of the important Supreme Council members.