A yeast culture is kind of like a nuclear weapon in that one only needs to be less than an order of magnitude away from a calculated yeast cell count in order for it to be effective. Given enough carbon and oxygen, the difference in propagation time between 50 billion cells and 200 billion cells is 180 minutes at 25C.
With that said, your experiment also highlights something else I that have been championing on this forum; namely, that one should pitch at high krausen instead of waiting until the starter has fermented out. Cells that are pitched at high krausen are in better health than those that have reached quiescence. However, in your case, you demonstrated the difference in health between two different cultures that had reached quiescence. One culture had recently reached quiescence whereas the other had been in a quiescent state for an extended period of time. Yeast cell health declines as the cells get further away from high krausen.
Here's what really made the difference in lag times. In addition to increasing the size of the biomass, the starter gave the yeast cells time replenish reserves that had been exhausted during an extended period of quiescence. Additionally, the starter was propagated at room temperature, which is closer to 25C than the typical fermentation temperature. The lag time on the direct pitch would have been a fraction of the time that it was had you pitched at 21C/70F and waited for visible sighs of fermentation to appear before placing the fermentation vessel into your fermentation chamber. Yeast metabolism slows as temperature is decreased. Anything that slows yeast metabolism increases the the length of the replication period. However, in this case, slowing yeast metabolism was not necessarily a bad thing because low temperatures affect wild microflora more than they do domesticated brewing yeast strains.