Misinformation threatens our societies, but little is known about how the production of news by unreliable sources relates to supply and demand dynamics. We exploit the burst of news production triggered by the COVID-19 outbreak through an Italian database partially annotated for questionable sources. We compare news supply with news demand, as captured by Google Trends data. We identify the Granger causal relationships between supply and demand for the most searched keywords, quantifying the inertial behaviour of the news supply. Focusing on COVID-19 news, we find that questionable sources are more sensitive than general news production to people’s interests, especially when news supply and demand mismatched. We introduce an index assessing the level of questionable news production solely based on the available volumes of news and searches. We contend that these results can be a powerful asset in informing campaigns against disinformation and providing news outlets and institutions with potentially relevant strategies.