Buddhism holy books are written in prakrit which is derived from sanskrit. Nepal is basically part of indian subcontinent in terms of culture, race and language. Buddha himself travelled all over Indian subcontinent and gained Buddhahood not in Nepal but in current India.
It's funny how Indians like to claim Kung Fu is from India due to buddhism.
Yet China has a far better claim buddhism than India because buddhist in India disapeared while it thrives in China but China is the only country in the world to have all three buddhist traditions (Mahayana, Therevada and Vajrayana) coexist natively.
Also Buddha is nepalese and the sites that are in India belong to the Shayka civilization which is culturally Nepalese therefore I refuse to believe Buddhism is an Indian religion.
Entire mythology of Buddhism including all the names and concept comes from Hinduism. Buddhism is basically an alteration or answer to hinduism and what Buddha thought was wrong with it.
So, its disingenuous to say Buddhism is not Indian.
Better question is why did the Chinese adopt a foreign religion when they had perfectly good local religion like taoism. Chinese should maybe abandon buddhism and go back to local religions. Think about that.