Yeah, it's me again.
Yes, I think creating a new group with extra permissions is a good way to give access to a private forum.
I agree it would be better to have a more accurate message. If I remember correctly there's an "if" statement in the code somewhere checking several reasons why a user might not have access, and if it fails it shows that one message. I guess it's probably been that way for a long time, and banned users is probably the most likely cause (because really there's not much reason to have a group with no permisssions

.
This is probably obvious now, but you could create yourself a "regular" user account so you can log in and see what a normal user would see.