I believe Verin is part of a secret society within the Ajah's. There is evidence in RJ's Guide to the WOT that that "Ajah" originally meant a grouping of AOL AS, male and female, that combined to work together on a problem. Later, it stood for any gathering of pre-tower AS. Several "ajah's" were forcibly brought into the tower after the strongest resistors to tower leadership were stilled. Then, the Tower re-defined and created the Ajahs as we read of them currently. I believe Verin is part of an ajah (old definition) that is dedicated to a higher purpose than the "White Tower" (the Creator, preserving AOL knowledge, etc). If Coriannin were part of this group, it would help explain how Verin came upon the ring ter-angreal (a ring that the Tower knows nothing about). Perhaps the notes Coriannin left reveal too much of this group and could not be shown to Egwene (Verin considered sharing the notes, but declined after some consideration). Moiraine may suspect the existence of such an organization: she obviously knows Verin dances to her own tune on a number of Aes Sedai issues. With the threat of AS members of this group being stilled, or harshly disciplined at the least, I think such an organization would need to be as secretive as the black ajah. If such a group exists, it is likely that very few sisters are a part of it (certainly fewer than are in the black ajah). I know several readers can probably add some "flesh" to these bones, but it is an avenue worth pursuing.