I think the simplest answer as to why others didn't figure it out was that they didn't want to, as it might prove unhealthy.

As for Verin, even if strengths were concealed at meetings, if she was on the SC for a long time (and I think she probably was), logical deduction would have proven useful in puzzling out who else was a SC member. Remember, no one had Traveling until the Books, so if the SC had regular meetings, Verin could easily cross reference who was missing from a meeting with who was out of the Tower. With enough meetings, she could puzzle out who was who pretty easily.