Can an iPhone 4 be in any way repaired in a different country than from where it was purchased?

I purchased an iPhone 4 in the US around 2 years ago. It recently got a hardware fault (-1) iTunes error. It has run out of warranty so I was wondering if it could be fixed in the country I am in now? I live in New Zealand. App support said it couldn't be repaired in NZ it had to be shipped back to the US.

Could it be fixed by a third party repair service? Or could I do it myself? Maybe I could buy the parts then open it up and repair the so called 'baseband hardware problem' myself.

Also the back camera and the lock button don't work. As far as I know there is no water damage.

Thanks