The terms for AppleCare+ don’t say that, at least not in the US. They only say that if you get service in a different country you have to pay whatever the fees are in that country (which might be different than the fees where you bought the phone) and that if you need service that isn’t available in that country you might be on the hook to pay the costs of shipping the phone to a different service center, and that replacement parts might be a different version than what you originally had.

Please note that if you seek service under this Plan in a country other than your country of purchase, the service fee will need to be paid in that country’s currency and at that country’s applicable rate – for further details, including regarding applicable fees by country, please visit apple.com/legal/sales-support/applecare/applecareplus/ and select the appropriate device and location in which you seek service to view the applicable terms and Policy Excess fees.

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Service will be limited to the options available in the country where you request service. Service options, parts availability and response times may vary. If service is not available for the CoveredEquipment in a country that is not the country of purchase, you may be responsible for shipping and handling charges to facilitate service in a country where service is available. If you seek service in a country that is not the country of purchase, you must comply with all applicable import and export laws and regulations and be responsible for all custom duties, V.A.T. and other associated taxes and charges. For international service, Apple may repair or exchange products and parts with comparable products and parts that comply with local standards.