I didn't mean to offend - I didn't think you literally thought babies head were like plasticine, and you are far from the only one who thinks this is how baby's heads flatten, but the literature is really clear. I'm quite passionate about educating other parents, too.
Yes, advice is to turn baby's head to the other side. This works for the 60% of babies who were not in danger of flattening in the first place. But for a baby with significant torticollis, turning the other way is physically impossible. Every parent who has been through Physiotherapy for their child's torticollis will tell you, it hurts them to turn their heads. You have to be really gentle with the stretching, and they often fight it. So repositioning - the dogma of the last 30 years - just does not work. This is why parents end up helmeting their babies - you can bet your life they tried repositioning prior to shelling out £2800! If they are asleep and you turn their heads they wake up. Or they just turn it back again. I know a woman whose mother moved in with them and stayed up overnight, all night every night, with a timer, turning the baby's head back to the non flattening side every 15 minutes. It didn't work, she flattened anyway.
The other issue is that if significant flattening is present, repositioning doesn't work to correct the asymmetry. In order to correct one side of "no growth", and one side of "overgrowth", we now need to reduce growth on the overgrown side and direct it to the flat side. This is how helmets work. It is also how The Perfect Noggin works - and the beauty of the PN is that even if the torticollis is not yet resolved, the baby cannot flatten, because there are no flat surfaces; the occipital bone sits in an anatomically correct contour.
The Back to Sleep campaign was started in the late 80s and for the last 30 years, the incidence of cranial asymmetry has remained unchanged. I think at this point it ought to be concluded that as a strategy, it remains somewhat lacking.