How was it China's fault? all experts agree on the same thing, the chinese wanted to negotiate, Nehru refused and sent his troops in to claim the disputed territory declaring that he will drive out all chinese. China's only goal was to keep the Indians out of the disputed territory and once they achieved that they declared a cease fire.
The chinese were also extremely nice to Indian POW's, and they even returned all their captured weapons free of charge.
YouTube - The crushing moment: China India 1962 war - Part 2
The only people who have any claim to this land is Tibet of the kingdom of Ladakh which no longer exists. These people almost have 100% nothing to do with Hindus or pakistani.
Obviously you have no idea how international dipomacy work, but anyways.Akasai Chin is also primarily Tibetan, They don't look like Hindus to me. This area has always been part of the tibetan empire till it was conquered by the kingdom of Ladakh.
By your logic, then Uyghur has a legitimate claim of Xinjiang because they do not look like Chinese. Mongolian has a legitimate claim over entire China, since Chinese have practually the same DNA as their, and China used to be part of their empire. But things do not work that way. There are big chunk of Russian far east that was conceded to them during Qing Dynasty, should China claim those back now too? Do you know how China proper looks like? What happened has happened, and what has been done had been done. Stop living in the dream of your past and face the reality.