1) Embryos are considered a separate human life, deserving of legal protection (I disagree with this, but that's the view ES research opponents take)
2) In order to get ES cells, an embryo must be destroyed
3) Therefore, current methods of ES research are immoral
The great-grandparent post came close stating (or maybe he was stating, I'm not sure) that any research on human cells was playing god and therefore immoral. He was saying that even this new method of stem cell derivation would be opposed by those who oppose ES research for that reason. I disagreed - it's the embryo destruction that's the problem, not the idea of stem cells itself. Embryos can become an individual human, amniotic stem cells are (right now) unable to.
Part of the problem might be that I study this sort of thing, so it's tough for me to tell how much is too dumbed-down and how much is insufficiently dumbed-down. The inner cell mass of a mammalian embryo, which is the part the ES cells are derived from, is the part that becomes the new individual. However, saying that ES cells can become a new individual was likely poor and unclear wording on my part.