Labeling news as fake is a recent phenomenon occurring predominantly online, and increasingly in political online environments. This paper investigates the influence of expressed doubt in media independence on trust in news reports on climate change, and on trust in more scientific sources. Evidence from a laboratory experiment does not suggest that reading a media-critic statement affects perceived trust in the media-, or the scientific source reporting on climate change. Bayesian analyses provide a practical interpretation of the null findings, and further analyses show that the statement decreases trust in the scientific source when subjects read the media article first. Findings add to the emerging literature on fake news, echo chambers and filter bubbles, suggesting that labeling stories or outlets as fake news may not affect public opinions. Further research is needed to substantiate this conclusion.