Interplanetary solar radio type III bursts provide the means to remotely study and track energetic electrons propagating in the interplanetary medium. Due to the lack of direct radio source imaging, several methods have been developed to determine the source positions from space-based observations. Moreover, none of the methods consider the propagation effects of anisotropic radio-wave scattering, which would strongly distort the trajectory of radio waves, delay their arrival times, and affect their apparent characteristics. We investigate the source positions and directivity of an interplanetary type III burst simultaneously observed by Parker Solar Probe, Solar Orbiter, STEREO, and Wind and we compare the results of applying the intensity fit and timing methods with ray-tracing simulations of radio-wave propagation with anisotropic density fluctuations. The simulation calculates the trajectories of the rays, their time profiles at different viewing sites, and the apparent characteristics for various density fluctuation parameters. The results indicate that the observed source positions are displaced away from the locations where emission is produced, and their deduced radial distances are larger than expected from density models. This suggests that the apparent position is affected by anisotropic radio-wave scattering, which leads to an apparent position at a larger heliocentric distance from the Sun. The methods to determine the source positions may underestimate the apparent positions if they do not consider the path of radio-wave propagation and incomplete scattering at a viewing site close to the intrinsic source position.