Hi, the short answer is no, you don't have to cable front every other cable. It will look different butt still a cable. I recently made my niece a headband was was cabled like this and I was skeptical too but it works.
I will try to find a picture for you. Or if you have the book, One Skein Wonders you can find the pattern for the headband I made on page 47.
OK, the easiest way for me to show you the differrence is on Ravelry. Go to user Nowandthen and look up the headband on their projects. It does the cabling the way your pattern says. Though I think it is done as a C3F.
Then look at my projects (ID is Marj) and see my Coronet hat and cable scarf and you will see the more traditional cable with alternating C3F and C3B.