Ah, so when commodity prices go up, the index goes down. So for a decline in the index, we could be talking not about a decline in food production, but a rise in price.

Which everyone knows already - we're producing more food than ever, but it's getting more expensive, price pushed up by demand for livestock and biofuel feeds.

The 2003 quote, rather than being "out of date" is very relevant; 2003 is the year of the lowest index in your given series. So even when food was most scarce and/or most expensive, still the DG of the FAO was saying there was plenty.

Just take a look at the FAO's world food situation page. A glance down the reports and articles tells us that the issues are a shortage of fertiliser, and rising prices. Not a lack of food being produced. There's also a fear that some regions could lose production due to climate change. Could - not will.

A closer look at one of the articles gives us a few key quotes.

[...] the observed long-term decline in real prices could come to halt, signalling a structural change in agricultural commodity markets.[...] However, it is too early to determine whether the observed change is permanent or temporary.[...]

[There were] weather-related production shortfalls [eg drought in Australia leading to lower production...]

Stocks. Another factor on the supply side that has had a significant impact on the markets recently is the gradual reduction in the level of stocks, mainly of cereals, since the mid-1990s. [...] There have been a number of changes in the policy environment after the Uruguay Round Agreements that have been instrumental in reducing stock levels in major exporting countries: the size of reserves held by public institutions; the high cost of storing perishable products; the development of other less costly instruments of risk management; increases in the number of countries able to export; and improvements in information and transportation technologies. [ie, they haven't stored as much grain because it's expensive to do so and they haven't really needed to]

Changing structure of demand. It is widely accepted that economic development and income growth in important emerging countries have been gradually changing the structure of demand for food commodities (especially in China and India) [ie the Chinese and Indians are eating more meat; the article says it takes 7.5-8kg of grain to produce 1kg of beef, with an obvious effect on prices...]

Biofuels and agricultural commodities. The emerging biofuels market is a new and significant source of demand for some agricultural commodities such as sugar, maize, cassava, oilseeds and palm oil. These commodities, which have predominantly been used as food, are now being grown as feedstock for producing biofuels. Significant increases in the price of crude oil allow them to become viable substitutes in certain important countries that have the capacity to use them.

And so on. Nowhere do they mention "lower production" on a global scale. This or that country produces more or less, but the total production of grains, oils, sugar and so on continues to rise.

Nobody is going hungry because there's not enough food. They're going hungry because their area has trouble growing it (eg in the Sahel in West Africa) and because they're too poor to buy it.