By design on an inline cell comment, a user cannot inline edit another users comment.
In order for a user to edit another users comment as of version 188.8.131.52 and lower a user (or Application Role) must have the privilege of "Can mark comments as Approved".
Once this privilege is established a user can edit another users comment in the immediate inline cell form field.
Alternatively, a user can select the menu option of the ILC and edit the comment.
Future privileges may be created to delineate this functionality with a more descriptive privilege option.