I assume that the underlying study breaks the population down into quintiles or deciles based on income and then looks at spending on housing for each group, but it's not clear from the article.
If you simply compare average income to average housing costs you're going to get a skewed result. A software engineer living in the Bay Area could be well over the national average for housing (40% or 50% of income, maybe more in some cases) but they're definitely not contributing to an increased poverty level.
Another way of looking at this is that California's poorest counties are in the Central Valley. I suspect this is also where California's cheapest real estate is at.