The estimate returned by the calculator (a Bayesian beta-binomial conjugate analysis) requires that there is no conflict between the prior and the likelihood. When there is a prior-likelihood conflict then the estimate may be biased towards the prior and should not be used. One way of assessing the presence of the a prior-likelihood conflict is to examine the plot of the prior, likelihood, and posterior. If the prior and the likelihood overlap considerably then there is no prior likelihood conflict. Another way of assessing the presence of the a prior-likelihood conflict is to use a formal test (in the BayesSQUEAC calculate the z-test is used). The null hypothesis is that the prior and likelihood do not conflict. If the p-value is small (i.e. p < 0.05) we would reject the null hypothesis of no conflict (i.e. there is a conflict). In your example p = 0.8093. This means that there is no evidence to support the existence of a prior-likelihood conflict and it is safe to use the estimate. If you examine plot of the prior, likelihood, and posterior for the survey that prompted your question you should see that there is a large overlap between your prior and likelihood. I hope this helps. BTW : Congratulations on achieving a high coverage.