Strategic actors often manipulate others’ beliefs not by lying outright, but through selective truth-telling—also known as lying by omission or paltering—by withholding crucial details while avoiding falsehoods. For example, a pharmaceutical-funded investigator might truthfully report that some patients improved, while omitting that most did not. To guard against such selective disclosures, listeners must engage in epistemic vigilance: critically evaluating information in light of the speaker’s potential agenda. In this work, we develop a Bayesian computational model of this process. We present three key findings: (1) credulous listeners who assume informative intent learn quickly in cooperative settings but are highly susceptible to persuasion; (2) vigilant listeners who account for potential bias more accurately recover the underlying true world states, even from purely persuasive speakers—albeit with slower convergence; and (3) this robustness stems from their ability to discount biased framings by reasoning about alternative utterances the speaker could have chosen otherwise.