Internet-distributed hardware-in-the-loop (IDHIL) simulation integrates HIL setups between geographically dispersed engineering teams and fosters concurrent systems testing early in the design process. The question naturally arises: what is the cost in fidelity incurred by distributing the simulation across Internet links? The degree to which an Internet-distributed simulation loses fidelity relative to a single-location HIL setup is referred to as distortion in this paper. Various factors affect distortion, including the Internet's delay, jitter, and loss, as studied extensively in the literature. Additional considerations, however, such as the coupling points, i.e., the particular points at which the system model shall be divided to enable distribution across the Internet, also affect distortion. The aim of this paper is to turn coupling point selection into a design decision that can be used to minimize distortion. To quantify distortion, a frequency-domain metric is proposed using a linear systems framework. This metric is then used to analyze how the choice of the coupling point affects distortion, and it is also linked to a sensitivity function, which is easier to interpret physically. This analysis can be used in an ID-HIL setup to pick a coupling point that gives minimal distortion, and is the first step towards analyzing the trade-off between stability robustness and transparency in an ID-HIL system.