Translation:Chinese tea culture is famous.
Actually, I think the original version sounds much better:中国茶的文化很有名。
In your version 中国的茶文化很有名* the 的 sounds like it's in the wrong place.
Although 中国茶 is a name of a kind of tea, I agree. I don't think 中国的茶文化 is correct, if 的 has to be placed in between at all it should be 中国的茶的文化, my Chinese teacher always told us not to be afraid to use more 的 in such situations even if it doesn't sound as smooth.
"The culture of Chinese tea is famous." should be accepted. It's nothing more than a reordering of the official answer via "of".