They are right in this case.
In 1952 Alfred Sauvy, a French demographer, coined the term Third World which he described as the people of the world that are "unknown, exploited, and scorned." In pre-revolutionary France, the first two estates were the nobility and the clergy; everybody else was the third estate. He joked that the capitalist world (First World) compared with the nobility and the communist world (Second World) with the clergy. The First World consists of wealthy capitalist, formerly industrial, countries and the Second World of the former communist and industrial countries. Third World countries are all the other countries and they have always included capitalist (e.g., Brazil) and communist (e.g., Cuba) countries, and very rich ..... http://www.uwec.edu/geography/Ivogeler/w111/3world.htm
USNews usage was more common, and you definitely could mix many of the formerly Communist states into the same category as Argentina and Mexico, although other Communist states were necessarily third-world hell-holes.
There's even a term "fourth world" that refers to hopelessly impoverished, or even "failed" states. Examples are Haiti, Bengla Desh, Eritrea, etc.
Wikipedia continues to be untrustworthy.