Telepresence systems have the potential to overcome limits and distance constraints of the real-world by enabling people to remotely visit and interact with each other. However, current telepresence systems usually lack natural ways of supporting interaction and exploration of remote environments (REs). In particular, single webcams for capturing the RE provide only a limited illusion of spatial presence, and movement control of mobile platforms in today's telepresence systems are often restricted to simple interaction devices. One of the main challenges of telepresence systems is to allow users to explore a RE in an immersive, intuitive and natural way, e.g., by real walking in the user's local environment (LE), and thus controlling motions of the robot platform in the RE. However, the LE in which the user's motions are tracked usually provides a much smaller interaction space than the RE. In this context, redirected walking (RDW) is a very suitable approach to solve this problem. However, so far there is no previous work, which explored if and how RDW can be used in video-based 360° telepresence systems. In this article, we conducted two psychophysical experiments in which we have quantified how much humans can be unknowingly redirected on virtual paths in the RE, which are different from the physical paths that they actually walk in the LE. Experiment 1 introduces a discrimination task between local and remote translations, and in Experiment 2 we analyzed the discrimination between local and remote rotations. In Experiment 1 participants performed straightforward translations in the LE that were mapped to straightforward translations in the RE shown as 360° videos, which were manipulated by different gains. Then, participants had to estimate if the remotely perceived translation was faster or slower than the actual physically performed translation. Similarly, in Experiment 2 participants performed rotations in the LE that were mapped to the virtual rotations in a 360° video-based RE to which we applied different gains. Again, participants had to estimate whether the remotely perceived rotation was smaller or larger than the actual physically performed rotation. Our results show that participants are not able to reliably discriminate the difference between physical motion in the LE and the virtual motion from the 360° video RE when virtual translations are down-scaled by 5.8% and up-scaled by 9.7%, and virtual rotations are about 12.3% less or 9.2% more than the corresponding physical rotations in the LE.