India hasn't been a unified country for that long, so it might be a little hard for Indians to truly appreciate our voluntary clinging to the idea of "great unity", and after being humiliated by almost all the major powers in recent history, one after another, you can bet the Chinese government, especially the PRC, would not let a square-inch of territory slip through its fingers.
And for that matter, no, Tibet was not a free nation, it has been a vassal state of the Qing dynasty for hundreds of years, and more than one emperor had sent troops there to insure our sovereighty, more often than not at the very requests of the then Dalai lamas.
The one thing people can argue for Tibet's independence is whether the PRC government had the right to inherit Tibet's territory from the Qing dynast and then the ROC, but since no one seemed too upset when USSR claimed the legacy of Tsar Russia, I don't see the problem.
And speaking of misinformed, aint we all?