Randomised controlled trials (RCTs) aim to rigorously examine the cause-and-effect relationship between disease treatment and its clinical outcome. The success of this endeavour depends on the absence of errors in the applied RCT methodology. To identify potential errors, RCTs undergo critical appraisal using trial appraisal tools. Currently, the most recommended tool for assessing the risk of systematic error (bias) in RCTs is the second version of Cochrane's Risk of Bias tool (RoB 2; Cochrane, London). This review shows that the application of the RoB 2 tool is based on inductive verificationist reasoning, which leads to invalid circular inferences or a lack of justification for RCT result validity. More importantly, inductive verification also allows formal logical justification that RCTs with an overall 'low risk of bias' rating do not require critical re-appraisal in the future. This poses a practical risk, preventing the re-appraisal of high-bias risk RCTs that were erroneously rated as 'low risk of bias' in the past and allowing the conclusions of such RCTs to continue guiding clinical practice. In contrast, deductive falsificationist reasoning is free from these shortcomings and may provide a more robust logical basis for the critical appraisal of RCTs. Classical critique of deductive falsification is insufficient for dismissing it as a basis for RCT appraisal.