Is it really provably superior to anti-aliasing on a same-rez CRT?

I don't know about "provably", but the argument is straightforward. When you treat each sub-pixel separately, you triple the horizontal resolution of your monitor. You can't do it on a CRT because the alignment isn't tight enough, but on an LCD the alignment is perfect. The trick is to take advantage of the extra horizontal resolution without introducing rainbows. For starters, when you've got RGBRGBRGB subpixels, there's no rule that says a pixel needs to start on the R and end on the B. If you take any three adjacent sub-pixels and move them up and down together, you still see grey. I imagine the secret sauce is knowing when you can get away with this, and how much you can push it before the user notices. I'll bet they did extensive user studies. Adobe CoolType, for example, comes with a dialog that gives you very, very different results depending on how you configure it.