My iphone 6 suffered quite a small knock and the display cracked. It's not too bad and is a small crack rather than the 'shatter' type damage.
I checked the apple website for details and in the USA they fix the screen for $109USD (or $79 if you have applecare) ( https://www.apple.com/support/iphone/repair/screen-damage/ )
But, on ringing my local apple service agent said apple nz do not fix broken screens. You basically must buy a new phone.
So, if your iphone 6 screen suffers any damage at all then apple nz will not fix as it is too hard.
I wonder why apple US can do it and not apple NZ. In the US you can take the phone into the apple store and they have an onsite tech who repairs it right away.
Looks like a trip to the insurance company.