For safety-critical systems, it is essential to quantify the reliability of the assumptions that underlie proven guarantees. We investigate the reliability of the assumptions of the SPIDER group membership service with respect to transient and permanent faults. Modeling 12,600 possible system configurations, the probability that SPIDER's Maximum Fault Assumption will not hold for an hour mission varies from less likely than 10{-11} to more likely than 10{-3}. In most cases examined, a transient fault tolerance strategy was superior to the permanent fault tolerance strategy previously in use for the range of transient fault arrival rates expected in aerospace systems. Reliability of the Maximum Fault Assumption (upon which the proofs are based) differs greatly when subjected to asymmetric, symmetric, and benign faults. This case study demonstrates the benefits of quantifying the reliability of assumptions for proven properties.