Today, when my permissions are set to edit, but the permissions for Anyone on the Internet are set to something more restrictive, the icon shows the globe. I would not expect this to be the case, since the globe usually implies Anyone on the Internet can edit.

The reason for this request is that it's confusing as is. I was working with a user on their board and asked for edit access. When I saw the globe, I got concerned thinking he opened it up to be edited by anyone. That's not what I meant to ask for! Turns out, that's just the icon I see when I have access.

For the sake of clarity and trust, we should reserve that icon for the specific permission of Anyone on the Internet can edit. And we can think of a new icon to show in this specific case, where my permissions differ from the Internet's.