In total, in eight out of the 14 pairings of disease and country they looked at over the course of three years, Wikipedia visits were an accurate guide to disease outbreaks. That's despite their model, largely developed as a proof-of-concept, being relatively crude – it only looks at a small selection of articles potentially related to the diseases, and (because the Wikipedia logs don't track visitors geographical locations) the researchers had to use the language of Wikipedia articles as a rough guide to where users were.
In addition to "nowcasting" the state of diseases (accurately tracking their incidence day-to-day), the successful models were also able to forecast with some accuracy how the outbreaks would play out. Much as with Google's Flu Trends, that could be because people are likely to search the internet for information about their symptoms before they go to their doctor.
However, other disease/country pairings weren't successful, such as cholera in Haiti, Ebola in Uganda and the Democratic Republic of Congo, and HIV/AIDS in China and Japan. The researchers think this might be due to reasons such as noise in the Wikipedia data, the diseases either changing too slowly or with too few cases for a pattern to emerge, or the country having realtively poor internet connectivity (as is the case in Haiti).