According to your screenshot, the checklist is set to 'teacher only' mode.
This means that students (i.e. users with the 'updateown' capability) are not able to update the checklist.
The only person who can update the checklist is a teacher (i.e. someone with the 'updateother' capability), who can go via the report, then click on the 'magnifying glass' icon then update the checkmarks for another user.
I can see where the confusion may lie, but basically you have redefined the capabilities of the teacher to match those that would normally be given to a student, which means they are now equivalent to 'student's as far as the type of checklist they are able to update - i.e. they can only update checkmarks if the checklist is set to 'student only' mode in the settings.
Just to clarify, in case I haven't written enough already:
Student only = users with 'update own' capaibility can update their own checkmarks
Teacher only = users with 'update own' capability are listed in the report and users with 'update other' capability can update the checklists of the 'update own' users
Teacher and Student = users with 'update own' capaiblity can mark off items on their checklist, but the actual progress is not updated until a user with 'update other' capability updates the checklist with their opinon on the marks.