Just to elaborate a little bit more as this is a topic that has interested me for awhile, the big thing that is happening when you "arch hard" in the squat is you are taking some stress off of the spinal erectors and transitioning that force into the spinal column via bone stacking where the stability is not coming from the tension in the muscle but from the bone on bone contact. Just like butt winking forward and letting the spine flex under axial loading increases risk of injury (herniated disc) so does the hyper extending of the spine as well. http://www.spineuniverse.com/sites/default/files/legacy-images/facetjoints2_250-BB.jpg
The concern with neck positioning however, has a few other mechanisms relating to it. Robertson has written about the extensor reflex, where the action in the cervical spine is reflected in the lumbar spine, so if you look straight forward the lumbar spine extends as well putting you into anterior pelvic tilt while inhibiting the glutes. Charlie Weingroff explains that by packing the neck into a neutral position but turning the eyes up and "looking through your eyebrows" you can regain the long spine position and better express your hip strength. Even though his writing was more directed at hip hinge type movements, I believe Rippetoe is using this same reasoning in his coaching while ommitting eye gaze.
Alright, I'm done rambling, just food for thought