Hi,
According to WordPress built-in permissions logic:
– User can not edit any posts if he does not have ‘edit_posts’. User can not edit posts created by other users if he does not have ‘edit_others_posts’.
Thus, ‘edit_posts’, ‘edit_others_posts’ capabilities are required both in order user can edit posts created by other users.
URE shows ‘with author user ID’ field for user or role if it can at least ‘edit_others_posts’ or ‘edit_others_pages’ and restricts posts available for editing by posts created only by users which ID are listed in this field.
I can just suppose according to your description, that some other plugin may change default WordPress permissions logic. Try temporally deactivate all plugins except URE Pro and test what posts are available for editing to restricted user. If it will work as expected, activate plugins back one by one with new test in order to isolate a conflict.