I thought it was the basilisk's direct stare that killed people and those who were Petrified stayed alive because they only saw its reflection, or saw it through something else (like Colin Creevey with the camera, or Justin What's-His-Face through Nearly Headless Nick)? And isn't Prof. Binns (History of Magic, I think) a ghost who died in his sleep of old age or something?

Hmmmm... I have long wondered about the logic of this, myself.