Why would people share news they think might not be accurate? We identify a factor that, alongside accuracy, drives the sharing of true and fake news: the ‘interestingness-if-true’ of a piece of news. In three pre-registered experiments (N = 904), participants were presented with a series of true and fake news, and asked to rate the accuracy of the news, how interesting the news would be if it were true, and how likely they would be to share it. Participants were more willing to share news they found more interesting-if-true, as well as news they deemed more accurate. They deemed fake news less accurate but more interesting-if-true than true news, and were more likely to share true news than fake news. As expected, interestingness- if-true differed from interestingness and accuracy, and had good face validity. Higher trust in mass media was associated with a greater ability to discern true from fake news, and participants rated as more accurate news that they had already been exposed to (especially for true news). We argue that people may not share news of questionable accuracy by mistake, but instead because the news has qualities that compensate for its potential inaccuracy, such as being interesting-if-true.