Sponsorship bias occurs when the financial interests of funders of scientific research influence claims made by scientists, especially in peer-reviewed publications. This article examines the relationship between sponsorship bias and misleading claims, understood as claims that are not necessarily false but which encourage those exposed to them to infer false conclusions. Misleading claims are relevant to how the term "bias" should be understood and thereby to evaluating a recent dispute about whether there is evidence of sponsorship bias in clinical research on statins. The concept of inferential asymmetry is introduced as an aid for understanding the relationship between misleading claims and sponsorship bias.