Power Hardware-in-the-Loop (PHIL) testing enables the validation of grid-connected converters under realistic conditions by interfacing physical hardware with emulated grid scenarios. The accuracy of such tests depends critically on accurately representing the electrical grid at the point of connection. This work investigates the impact of physical versus emulated grid impedance in PHIL setups, with a focus on transient events such as voltage magnitude and phase jumps. Firstly, the effects of real-time simulation limitations - including sampling, digital filtering, and system latency - are analysed. Secondly, the influence of varying the physical-to-emulated impedance ratio is systematically evaluated using PHIL experiments with both grid-following (GFL) and grid-forming (GFM) converters. A novel current correction method is introduced to compensate for phase delays caused by digital filtering, ensuring that physical and emulated currents align while retaining noise suppression. Results show that purely emulated impedance can lead to oscillations or instability, particularly in GFM converters. Introducing even modest amounts of physical impedance (≈25%) substantially improves steady-state and transient behaviour, reduces overshoot, and stabilizes system response. These findings provide practical guidance for designing robust PHIL experiments where accurate transient performance and physical realism are critical.