Okay, I created a new Project for an author o' mine. It was virgin (no reports published to it...ever), still had that "new 'database row added' smell". I set the "All Users" permission to Interactor and selected "Assign Permission to Contents". He couldn't see his Project to publish his report ??? So I deleted the User/Group completely and then re-added the "All Users", set its permissions to "Interactor" again, but I didn't assign all permissions. He still couldn't see it. So I checked the permissions to "Publisher" -- the only change that this makes in terms of permissions is that it sets the "Write/Web Save" permission to true. BAM! He was able to see his new Project and publish to it.
At first blush this seems odd. By default, the "Write/Web Save" permission for Interactor is set to "Inherit" (which, by the way, I find confusing at the Project level because there's nothing for a Project to inherit in the first place!). Anyway, so even a user who had Publisher and Interactor rights still needs to have the project they're saving to have its permissions set to "Write/Web Save".
This must mean ALL Projects MUST have their "Write/Web Save" set to true in order for Publishers to upload their reports but then they ALSO have to then set that same permission in their workbook to false if they don't want others to publish over it.