It seems to me the study says spanking is more common amongst poorer families, which doens't seem to surprising, however, there is already a well-known correlation between wealth and intelligence, mostly from wealthier people tending to be intelligent and thus have both their wealth and brains to aid them in making their kids smarter. So you'd expect to see spanking and intelligense inversely related even if spanking has no effect on intelligence.

What bothers me about this study is it seems, as you say, biased. The better choice, and the simpler and easier one I think, would have been to administer IQ tests to parents and child, and ask them if they use spanking regularly and how frequently. If it has any significant impact it should show up very blatantly when mapping the intelligence of children versus the intelligence of their parents when comparing spank vs non-spank.

Since this wasn't done, I wonder why not, since it seems far simpler in terms of resources and far more likely to indicate direct causation or a lack thereof.

It may be true though, but I suspect the main reason is different then implied. Spanking doesn't make kids dumber, spanking is more liekly to happen to children who are already in an environment less likely to promote scholastic tendencies. They could just as easily have done a study saying 'direct sunlight promotes athleticism' because most athletes spend more time out in the sun, it doesn't mean sunlight grows muscles. Or 'direct sunlight makes people stupid' because most budding scholars spend more time indoors reading.