Most horrible correlation argument

The above is a graph that posted was by NY times for an article- SAT Scores and Family Income.
Key conclusion of the article-
"Generally speaking, the wealthier a student’s family is, the higher the SAT score."
This has sparked a debate between two of my favorite economists- Greg Mankiw and Paul Krugman.

This is straight from Mankiw's blog-
"In essence, what I said was
1. People vary in their innate talents, as measured by, say, IQ tests.

2. More talented people tend to earn higher incomes.

3. More talented people tend to have more talented biological children--that is, talent is partially heritable.

4. As a logical implication of the above three points, the raw correlation of kids' SAT scores and family income conflates the true effects of family income with the biological transmission of talent."
--
Well, I cannot disagree more with Mr Mankiw because-
1. There is ample evidence in real life that suggests the opposite. Rich people have children who do not do well in examinations.
2. The argument is flawed in assuming that IQ is representative of the talent in a person. There are people who have become rich not because of the gift of intellectual endowment. There are several examples of people who did well just because of good management skills. I don't think IQ can be indicative of such things
3. The argument seems to suggest that children of rich people will do well in exams because their parent's are talented; it does not take into account the school conditions, factors such as intention of children to become intellectuals, etc. As an analogy- How,/When/Where the seeds of a rose plant are sowed determined the quality of the rose flower. If you plant the seeds in a desert and do not give any water, then the result is obvious.
4. I assume that the author of the original article will agree with the below statement:
"Transfer of money to dumb people will make the dumb people rich and hence intelligent"