Apple Care NOT International Warranty

I have bought all my Apple devices (iPhone, Macbook Pro, Apple Watches) in Hong Kong before I moved to the United States 2 years go. I bought all Apple Care with all my products. I was told Apple Care is INTERNATIONAL WARRANTY.

Last week, I needed my Apple Watch to be repaired. Genius Bar suggested me to do an express replacement. But when I called the Apple Care hotline, I was told since my Apple Care was bought in HK, I need to call HK to do a replacement or repair! US Apple will not honor the Apple Care! How does it classify as an international warranty?