A user is unable to edit a Solicit code that has security set to All Sites. The user's System Role has the appropriate permissions and has Site Security set to a particular Site.
This is working by design. A Solicit Code that is set to All Sites should only be able to be edited by a user who has a system role with the appropriate privileges and also has Site Security set to All Sites. To resolve, add the user to a system role that grants those privileges and is set to All Sites.