The only way to truly know what a bird died of is doing or have a necropsy on them. Taking a look inside the bird. This needs to be done on a freshly dead bird. And even then, sometimes you still don't know.
Yes, quail can die from the shock of being handled. Normally Coturnix are not all that nervous to be held like Bobwhites or Gambels, but it can happen. If you hatch them yourself, they will fair much better of you handle them like crazy as babies so they aren't as frightened to be handled. Adult...