'New Zealand where if you're "old" you're just not covered and you have to leave the country for basic things like dialysis, even though there are dialysis machines in the country'

Source for this? I know more than a few old people here on dialysis. The system will even pay to have a dialysis machine in your house if it's long term so you don't have to keep travelling to the hospital.

Care is universal, the only reason someone could be rejected is if they're not a New Zealand resident.