As the adoption of combined photovoltaic (PV) systems and battery storage systems (BSSs) for residential buildings increases, challenges for distribution network operators (DNOs) arise. Part of the attractiveness of investing in such systems stems from avoiding paying grid charges (GCs). Yet, the systems rely on the grid for PV feed-in and possibly contribute to PV grid integration challenges. Here, a bilevel optimization approach is developed to evaluate interdependencies between the DNO's decision of raising GCs and the reaction of PV BSS investors. The model allows DNOs to trade-off the effectiveness of different measures to foster PV grid integration and the danger of starting a self-reinforcing process, potentially leading to grid defection. Included are two case studies that show that the new equilibrium between DNO and PV BSSs comes at a price of raised GCs and larger PV system sizes. Yet, in either case study, grid defection is not a realistic scenario as the marginal value of additional self-supply decreases with higher GCs. Compared to PV curtailment by the DNO, or grid reinforcements, fixed feed-in limits and power-based GCs reduce oversizing of PV BSSs and provide an operational incentive for peak-oriented BSS operation.