I have now more or less solved the problem.
On my TV, CNN remains cut-off.
But I have also a hard-disk recorder and when I switch it on and go to CNN and then to "options" and further to "image settings", I can change the picture size with the other remote control so that CNN is not cut-off anymore.
Weird, right ?
The image setting menu for the hard-disk recorder (which is also from Samsung) has the button "screen adjustment" (which allows you to display the full HD-signal of a channel).
The image setting menu on my TV does not have this button for some reason.
It means that I always have to switch on my hard-disk recorder now if I want to watch the *full* CNN picture.