Getting insufficient access rights on object id for a user - only the role is different

I created a new role for users called "Phoenix"; users in that role cannot edit cases that they do not own. They're able to change the owner at which point they can edit; but otherwise cannot edit. The profile is the same as users in a role called "Call Center." Those users can edit the cases even if they don't own them. I have verified that if I change a "Phoenix" user to "Call Center" that user can then edit the case.

It's been awhile since I set up roles, but I didn't think they had anything to do with object level permissions. There are no permission sets assigned to the user, and the role is under the same hierarchy as "Call Center" and both roles are identical. I know there's something really obvious that I'm missing. All help greatly appreciated.