Custom of "Sati" in India

I am not a religious scholar, however with my limited knowledge about the history of India, I have the following thoughts about the custom of "sati".

The "custom of Sati" can be easily confused with the usual "ritual of cremation" in Hinduism. In the first case the woman either voluntarily or forcefully surrender herself to fire after her husband's death. The later is the ritual of cremation, where after death, the body is surrendered to fire. The western world finds both the rituals very cruel and insensitive. That might be because, it is very different from their culture. I am absolutely certain that the "ritual of cremation" is derived from Hindu religious scriptures. However, I sincerely doubt that the "custom of Sati" is according to Hindu religious guidelines. My analysis about "custom of Sati" is that, it must be as recent as the period of Islamic Invasion of India. The very first example of women voluntarily surrendering themselves to fire, can be found in the current state of Rajsthan. It is called "Johar" there. The Rajput women did "Johar" in order to avoid themselves falling in the enemy's hands after their men were defeated at war. The enemy which was "barbaric" that time and has a unique "negative" way of treating women. The unfortunate "voluntary incident of Johar", later went on becoming a "custom", where the society started "expecting an extreme sacrifice of her life" from a woman, after her husband's death (even though the death is NOT because of war). This custom was then called "Sati".