Because people keep referring to J R R Tolkien as a British author. He was born in Bloemfontein, South Africa!
As was Basil Rathbone, who was born in Johannesburg. Nigel Bruce was born in Ensenada, Baja California, Mexico, but that doesn't make him Mexican. And sisters Joan Fontaine and Olivia de Haviland were both born in Tokyo, Japan, but that doesn't make them Japanese. It is not where you were born, but the nationality of your parents that makes you what you are. I'm afraid.
I understand what you're trying to say, but this is a subject that is endlessly debatable. It's not as simple as what either you or Trevor have suggested, and that's not meant as disrespect to either of you.
My wife was born in Ireland, but raised from the age of 4 on in the U.S. She is 100% Irish by birth and by blood, red hair, freckles and all, but culturally she is very much Irish-American. Sure she grew up strongly influenced by her Irish heritage, but if you were to ask her or her family in Ireland they would consider her more of a yank.
So which is she? Irish? American? Certainly, she is a product of both. Ultimately it doesn't come down to place of birth OR parents, although both certainly play their part. Ultimately it comes down to what the environment dictates and what the individual considers himself/herself. Trevor was born and raised in South Africa, so for a number of reasons, not the least of which is what he considers himself, he is South African.
In Tolkien's case, I don't know that I would consider him South African. His work, his upbringing, his place in literature, seem decidedly British to me.