Why shouldn’t India recognize Tibet as an independent country?

Till 1951 Tibet was an independent country. India signed the Panchsheel agreement with Chinese at Beijing on 29 April 1954 hoping to peacefully solve all irritants between two neighbours in the spirit of Hindi-Chini-Bhai-Bhai. But ironically dug its own grave. Within six months the first Chinese incursion was reported in the Barahoti area of Uttar Pradesh in June 1954. This was followed by a hundreds of incursions which culminated in full-fledged war in October 1962.