I only mentioned that because it can be confusing. Usually a strong s/w may have a high PV intrusion by nature. You can also get PV by strong latent heat from convection. If you were to look at a cross section from the infamous 12/9/05 storm, you had strong stratospheric intrusion of PV aloft and at the surface from latent heat. Without getting too complicated, both acted to lower heights ahead of it and induce rapid cyclogenesis. I'm definitely not well versed in the topic, but that's the basic idea.