Is it true that phones bought overseas cannot be sent for repairs from an iStore in South Africa?

I have been having problems with the screen on my iPhone 5s recently.

After attempting to fix the problem with help from a user in the apple community, I decided to go to the local iStore (Walmer Park, South Africa).

They told me that my screen appears loose, but told me that they cannot send it for repairs from the iStore as I bought it in Germany.

Is this true?

How can I get it fixed as I don't want to send it to an unauthorized repairer?