The Spice algorithm (and Mike Ehglhart's LTSpice guru's enhancements) try to speed up the calculations by stepping over times steps where it thinks not much is going on. Some times the time step guesstimate fails, and the algorithm needs some guidance.
Alec's example poses a problem for the speed-up guess. He provides a 1mV change on top of a 3V level. The algorithm sees a node V(b) where relative to 3V, not much is changing, and thinks it can speed up by changing the time step to one that is large enough to skip over the detail. Specifying a max time step of 100ns force an evaluation of the circuit at least that often, so the detail of what is actually happening on node V(b) is revealed.