Refusal on Warranty Service of 2016 13-inch MacBook Pro Display by Local Authorised Service Provider

I am the owner of a 13-inch MacBook Pro computer that was purchased in December of 2016. Recently the display backlight of the above mentioned Mac device stopped working completely. Screen of the device is totally blacked out while the computer itself is in operational condition. I can still use it when connecting to the external monitor.

As I have read on apple.com website Apple has launched a 13-inch MacBook Pro Display Backlight Service Program. According to the information provided on the apple.com website Apple or an Apple Authorized Service Provider will service affected MacBook Pro units that are sold between October 2016 and February 2018 free of charge.

I have followed the instructions given on the apple.com website and identified that my device is covered by the above mentioned Apple program. On the website it is indicated that I should contact Apple Authorized Service Provider to have my MacBook Pro display serviced.

I contacted service provider listed on Apple.com for Georgia (Country in Europe, not US state) but company refused to service my laptop as it is not purchased at their partner store. When I bought this laptop this service provider company did not exist at all. Do they have the right to refuse the service? And what can I do? All other Authorised Service Providers are in foreign countries and they are very far from me. I can not travel more then 1000 miles to fix my laptop. So I am left without the service. Is that normal customer service? Should not Apple put pressure on their authorised service provider to fix my problem?

I am a long time Apple customer and use many devices/products from Apple. I do not think I deserve such an attitude from the brand.