This work investigates the impact of the ever-present electromagnetic interference (EMI) on the achievable secrecy performance of reconfigurable intelligent surface (RIS)-aided communication systems. We characterize the end-to-end RIS channel by considering key practical aspects such as spatial correlation, transmit beamforming vector, phase-shift noise, the coexistence of direct and indirect channels, and the presence of strong/mild EMI on the receiver sides. We show that the effect of EMI on secrecy performance strongly depends on the ability of the eavesdropper to cancel such interference; this puts forth the potential of EMI-based attacks to degrade physical layer security in RIS-aided communications.