Oh, well I must just be lucky (twice).
It definitely doesn't say it's international, but it doesn't say it isn't either.
Especially this clause:
IMPORTANT RESTRICTION FOR iPHONE, iPAD AND APPLE TV SERVICE.
Apple may restrict warranty service for iPhone, iPad and Apple TV to the country where Apple or its Authorized Distributors originally sold the device.
Also, the same thing happened with my Apple Watch. Replaced in the US under Applecare bought in Australia. I'm clearly very lucky.
Most Apple products have international warranties, including the Apple Watch. iOS devices and the Apple TV are exceptions.