Certainly that is a quick way to realize what a tiny keyhole ‘worldwide’ reporting is looking through, in many ways.
Though I agree that the reporting has been biased towards the negative, it's still the case that even if 75% of the world population experiences growth, the world can still be in a recession. That's because the world economy and the world population are two different things. Worldwide, a large population does not necessarily correspond to a large economic output.
The word “recession” refers to the shrinking of an economy--so when you're talking about a worldwide recession, you need to look at the worldwide economy.
Using 2009 numbers (which I concede are outdated, since China has outstripped Japan, among other things), the combined economies of every single country in Asia and Africa only account for approximately 30% of the world economy. The combined total of the United States and Europe account for 54%.*
So if the U.S. and Europe are in recession, at least 54% of the world economy is shrinking. That's a whole lot of economic loss worldwide. If the shrinking becomes severe enough, then the loss becomes more than what Asia and Africa can make up, even doing well. (For the math nerds: just to keep the economy in balance, i.e. neither growing nor in recession, for each percent of economic loss experienced by the U.S. and Europe, Asia and Africa would have to grow 1.8%. At a 2% shrinking level, there'd need to be a 3.6% economic growth. At 3% we reach a whopping 5.4% growth. That's darned hard to accomplish.)
Of course folks in the growing economies of Asia and Africa may not feel the effects of the worldwide recession--recessions do not affect everyone in the same way. But that doesn't negate that a worldwide recession may in fact be occurring.
Are our news outlets emphasizing the negative at the expense of the positive? Unfortunately, they tend to do that.
* I note that, left out of this discussion, are the economies of Canada, Mexico, the countries in Central and South America, Australia, New Zealand, and a smattering of small islands. They make up approximately 16% of the world economy.