Real lunkheads don’t graduate high school, they were already excluded. The argument you’re offering is at some level explaining why college grads earn more, and you’re suggesting it’s because they were better prepared for college, more likely to choose it, able to afford it, etc. That is true.
But your reasoning does not justify the comparison that was made in the article, nor does it explain why it’s valid. The statistic is comparing incomes for people who graduated college to people who graduated high school and not college. It doesn’t matter whether they made a “real” decision, whatever that means, or not. It doesn’t matter if some people didn’t consider college, or if some believed they couldn’t afford it, or if some chose not to go. The question the article posed is what is the financial outcome of going to college vs high school but not college, and for that it’s not okay to compare the bottom third of incomes of the college group to everyone else.
You’re rationalizing one of many ways to partition college grads. You’re failing to explain why it’s valid to choose a partition for one group and not the other. The article did not offer a reason to use the lower third of college grads.
If the useful analysis is in the middle, then why not compare the middle third of high school graduates to the middle third of college graduates? That would be valid, and it would show, accurately, that college graduates on average earn more. Comparing the bottom third of college graduates to all high school graduates is obviously choosing to lower the average income of the chosen college group. There is no evidence in the article that it was done to make the comparison more fair, it doesn’t appear to agree with your comments or share your reasons.
In case you missed it, I linked to a different version of the Fed’s report that spends a lot of time trying to tease apart some of the things you’re bringing up, but in a scientific and statistically valid way. They try to answer the tricky question of how much of the income premium of a college degree comes from the person, and how much is actually due to college. They are accounting for ability level, family income, family history of college attendance, race, and other factors that capture people’s ability to choose college, and separate their intrinsic skills from their education. https://news.ycombinator.com/item?id=37464064