Periodic perturbations with their period close to that of planetary rotation are observed in most of the magnetic field data from Saturn's magnetosphere. These data arise from the three spacecraft encounters with Saturn (Pioneer 11, Voyager 1 and 2). The long-held view that no planetary spin-periodic modulation was present in the magnetic field observations is thus not true. Here we present several new pieces of information obtained from a careful analysis of the magnetic field data in view of this peculiar periodic feature. First, by simple considerations of the magnetic field morphology, we argue that these perturbations cannot be directly due to the planetary intrinsic field. Also, we analyze by means of two-dimensional (2-D) hodographs the rotation of the magnetic field vector, expressed in an inertial planetocentric spherical polar coordinate system, and obtain a definitive argument against the possibility of a dipole tilt signature. In addition, we find that the inbound and outbound Pioneer 11 observations of the perturbations are nearly in phase (once the spatial distance is accounted for), indicating that this periodic feature is of a global nature. Finally, we discuss the fact that in the same data set, the magnetopause position in the dawn sector seems to be modulated in phase with the radial component of the perturbation magnetic field.