BTW, I double checked and I'm reasonably certain that the test failure happened because we started running the test on machines with a lower QueryPerformanceCou

BTW, I double checked and I'm reasonably certain that the test failure happened because we started running the test on machines with a lower QueryPerformanceCounter frequency (2.148 MHz) and the simulated counter values then created larger times that necessarily had less precision. I updated the post to include that. Note that the error bounds are only increased for those test values that are unrealistically large. The error bounds are as small as possible for the more "normal" test values.