Based on the wurtzite crystal structure, large (MV/cm) polarization-induced electric fields are known to exist in InGaN single quantum wells (SQWs) grown perpendicular to the GaN c-axis, and these fields may impact optical device performance due to the quantum-confined Stark effect (QCSE). In general, the QCSE has experimentally been found to be smaller than the theoretical value expected for a coherently strained InGaN QW, and subsequently the InGaN/GaN QW polarization field is often under-estimated as well. In this study, we measure the QCSE in modulation-doped, InGaN/GaN SQW LEDs. The well-behaved capacitance-voltage (majority-carrier) characteristics of these devices allow us to unambiguously determine the applied field with bias. With this analysis, we de-couple the QCSE from the QW polarization field and show that although the applied field approaches the opposing QW polarization field theoretical value (i.e., flatband), the QCSE remains too small. We propose a localized-hole picture of the InGaN QW which explains our optical and electrical measurements.