The reply to Sanderfur from Watkins on Duncan Green's FP2P has reassured me. The "demolition" (to quote commenter kwame nkrumah, which I thought was pretty good) is based on the idea that Sanderfur misrepresented statistics, ignores complex relationships such as preschool malnutrition and socioeconomic background, and is sweepingly ideological.
Watkins: "I have no interest in defending the indefensible quality of public education provided in many of the poorest countries. But when public education systems are broken they need fixing, not bypassing or franchising out to the private sector. And if we care about equity, there is no credible alternative to a public system that offers opportunity for all rather than choice for some."
As predicted, the image I am left with is that the issue of Universal Primary Education is much more complex than what the imaginary superhero of private provision could handle.
On the other side, Watkins' argument does have that more heartwarming feeling, which however floppy and immeasurable it may be, is something not to lose sight of, as it is a mark of our humanity.