Paragraph 1 states 46.2 million people lived below the official poverty level, and 10.4 million of those were working, so you conclude that the remaining "choose not to work". But the next line states that that first number includes children (at least 14 million http://www.nccp.org/publications/pub_912.html) and adults (including those unable to work for legitimate reasons).
Your other link doesn't show its math either. I'm feeling trolled.