My friend was denied service on his apple macbook that he purchased from the us...so not sure how valid is the international warranty claim
I have claimed warranty on overseas macbook purchases in the past and the reverse as well (i.e. warranty claim on a macbook purchased in India at a Apple US store)
For phones and accessories, I believe they will ask for a valid proof of purchase (but the warranty is still valid)
The last instance of I having to give an apple device for service was earlier this year - An airpod pro that was OOW but had a service bulletin extension.
The device was purchased in the US and when I gave it to the local store (In Pune), they did ask for a valid proof of purchase (incidentally, this was new).
A quick search on my mail account got me the fedex shipment delivery mail which I showed and that was adequate.
Do note that this was not even an invoice, just a shipment tracker for apple addressed to my name.
I did ask the store folks about this and they told me that for phones and certain accessories, they have been notified to check for presence of proof for item being a valid purchase .
This could presumably have to do with avoiding claims on stolen goods or outright gray market purchases.
Either way, the warranty remains valid in India (and elsewhere) as long as its a valid and legal purchase.
You may want to ask your friend what exact reason did they quote to refuse honoring the warranty.
