A Giffen good is something that people buy more of as prices increase, seemingly working against standard supply-demand theories. They're different from luxury goods, which have similar behavior; luxury goods are assumed to become more desirable as they become more expensive, since they are more status-providing. A Giffen good, however, is purchased more because as the price rises, the consumer can no longer afford to purchase higher-quality goods. Normally, these two effects -- wanting an inferior good less as it goes up in price, and having lower purchasing power as goods become more expensive on average -- combine so that you buy less of something as it becomes more expensive. For a Giffen good, the opposite is the case. Wikipedia, as always, is a good source of information on the subject:
So going back to the topic of the post: US Treasuries. In light of the S&P downgrade of US sovereign debt, investors have done a "flight to quality", where they allocate more money to investments with lower risk. Articles such as this mention how investors have "dumped equities in favor of traditional havens like gold and U.S. Treasury securities" (emphasis added). Yes, because of the credit downgrade, people are flocking to US Treasuries -- the very thing the credit downgrade was about.
While it seems counterintuitive at first, it makes sense when Treasuries are thought of as a Giffen good. In this case, all "prices" are measured in terms of risk. Investors roughly have a certain amount of risk that they are willing to take on, which represents their "budget". Treasuries are a cheap, but low quality, way of spending this risk budget. The credit downgrade increased the risk -- or "price" -- of Treasuries, and suddenly everyone's risk budget has been slashed. Because investors can't afford as much risk, they have to go back to buying the things that are cheap to satisfy their purchasing demands. This explains why, when the S&P says that US Treasuries are not as risk-free, rates actually decreased.
Of course, this all assumes that the credit downgrade is the only thing on investors' minds, and it only directly affects Treasuries.