The fact that some teacher can't see the correlations using an inappropriate plotting technique (he uses a scatterplot, he should use hexbin or other density plot) doesn't mean they aren't there. And the numbers he gathers and dismisses show the correlation actually does exist.

A simple numerical example, where the correlation is guaranteed (i.e., I took y=x+noise):

http://i.imgur.com/rrmUI.png https://gist.github.com/2183927

Most of the correlations he expects to find are present. They are noisy, but present.

The fact that in one case, reality is "contrary to what every teacher in the world knows" just suggests maybe teachers don't have a great grip on reality.

...if you took the teachers from the "worst schools" and put them in the "best schools" and vice-versa the results the following year wouldn't look noticeably different...Does that mean that teacher have no impact at all?

Not quite, but almost. It means that variation among existing teachers impact less than the size of measurement, and the current crop of teachers are basically interchangeable cogs.