Sayak you misunderstand the historical method. The historical method is not the same as the scientific method, because it depends less on empiricism and more on testimony and interpretation. A lot of history depends on testimony, because there are things you can know only through testimony e.g. An event that took place, such as a battle, you would only know from the reports of people e.g. The Greco-Persian wars, because they lack significantly in empirical evidence, we only know from Herodotus's account and based on Herodotus's information we can date the event. Similarly, the history we know of India we know through testimony, and it is testimony coming from multiple sources e.g. The historicity of Krishna, Rama, Mahabharata etc is not doubted even in the Jain and Buddhist puranas and chronicles, though they offer counter-perspectives on them, they do not doubt that they are real historical people. In much the same in Britain they do not doubt the historicity of King Richard.
AMT falsifies 10,000 years of Indian history, that is the records kept by the Indian people which speaks of continuous urban civilisation going back 10,000 years or more. The fact is we do have empirical evidence to back it up as well. So it is not just history based on testimony, but it is empirically validated too.