Some of the Eurocentric focus on history is partly because of the lack of historical documents from South Asia. I know that in India for e.g., recording a history of the region was never a priority, infact some of of India's early history is only known because of Chinese travelers noting down stuff in their diaries.

In modern times, producing an "Official" History of their region is a major undertaking that all nation states engage in. This is where they get to 'correct' the existing biases/stereotypes but a lot of nations lack the interest and frankly survey expertise to produce a decent and accurate History. I'd say that the West in general has been very good at documenting (sometimes with overflowing negative bias) the history of the 'other' much more than the 'other' has been, at documenting their own history.