The recent article ‘Satellite conjunction analysis and the false confidence theorem’ (Balch et al. 2019, Satellite conjunction analysis and the false confidence theorem. Proc. R. Soc. A475, 20180565) points to certain difficulties with Bayesian analysis when used for models for satellite conjuntion and ensuing operative decisions. Here, we supplement these previous analyses and findings with further insights, uncovering what we perceive of as being the crucial points, explained in a prototype set-up where exact analysis is attainable. We also show that a different and frequentist method, involving confidence distributions, is free of the false confidence syndrome.