Context. With its high complexity, large size, and close distance, the ringworld around GG Tau A is an appealing case to study the formation and evolution of protoplanetary disks around multiple star systems. However, investigations with radiative transfer models usually neglect the influence of the circumstellar dust around the individual stars. Aims. We investigate how circumstellar disks around the stars of GG Tau A influence the emission that is scattered at the circumbinary disk and if constraints on these circumstellar disks can be derived. Methods. We performed radiative transfer simulations with the POLArized RadIation Simulator (POLARIS) to obtain spectral energy distributions and emission maps in the H-Band (near-infrared). Subsequently, we compared them with observations to achieve our aims. Results. We studied the ratio of polarized intensity at different locations in the circumbinary disk. We conclude that the observed scattered-light near-infrared emission is best reproduced if the circumbinary disk lies in the shadow of at least two coplanar circumstellar disks surrounding the central stars. This implies that the inner wall of the circumbinary disk is strongly obscured around the midplane, while the observed emission is actually dominated by the upper-most disk layers. In addition, the inclined dark lane (“gap”) on the western side of the circumbinary disk, which has been a stable, nonrotating, feature for approximately 20 yr, can only be explained by the self-shadowing of a misaligned circumstellar disk surrounding one of the two components of the secondary close-binary star GG Tau Ab.