That's what professional says, then you have the elderly at home saying you need a pillow for your baby~ haha! It confused me at first too!
But I think it's to each own's preference. My 5 week old baby has been sleeping on an baby pillow in the night and without pillow in the day so he can turn his head freely. And he is doing good now, head still round!
My son is 5 months olds and at 10 weeks old he was diagnosed with a severe case of flat head.
This is what we were advised to do and it worked excellent- he no longer has flat head.
1- unlternate the ends of the cot/basinette where you place baby to sleep - this forces them to turn the head the other way when they wake to look at you. Baby may cry at first and find it harder to settle as it can hurt. I found it best at first to soothe baby to sleep before placing in the cot.
2 - we purchased a 2 in 1 sleeper - it has a special pillow fitted to it with a hollow in the middle for better fix.
Not sure what helped the most but these 2 things combined worked. The health nurse was so surprised at how quickly he recovered.