This makes sense. If a species is thriving and not under much selective pressure, it does not have to be optimized for its environment to survive. This allows for a larger amount of genetic variance. Most mutations either are maladaptions, don't cause any significant change or lead to death while relatively few confer an advantage. In addition, some adaptations may take many generations of mutation to actually provide an advantage or may need time to find a niche where a mutation that is a maladaptation in one environment may be an advantage in others (Sickle cell anemia gives resistance to malaria, Tay Sachs does the same for tuberculosis).

When selective pressures/shocks arise, there is a wider amount of genetic variance that can adapt to the new environment... a larger menu of options for survival, and this pressure acts as a feedback loop, further promoting that more mutations in that direction. Think of the pressures that led to the growth of the giraffe's neck. Perhaps it is this combination... allowing time for a species to thrive and have genetic diversity and shocks which select for and promote the evolutionary path