The interest in single-atom catalysts (SACs) is increasing, as these materials have the ultimate level of catalyst utilization, while novel reactions where SACs are used are constantly being discovered. However, to properly understand SACs and to further improve these materials, it is necessary to consider the nature of active sites under operating conditions. This is particularly important when SACs are used as electrocatalysts due to harsh experimental conditions, including extreme pH values or high anodic and cathodic potential. In this contribution, density functional theory-based thermodynamic modelling is used to address the nature of metal centers in SACs formed by embedding single metal atoms (Ru, Rh, Ir, Ni, Pd, Pt, Cu, Ag, and Au) into graphene monovacancy. Our results suggest that none of these SAC metal centers are clean at any potential or pH in the water thermodynamic stability region. Instead, metal centers are covered with H-ads, OHads, or O-ads, and in some cases, we observed the restructuring of the metal sites due to oxygen incorporation. Based on these findings, it is suggested that setting up theoretical models for SAC modelling and the interpretation of ex situ characterization results using ultra-high vacuum (UHV) techniques requires special care, as the nature of SAC active sites under operating conditions can significantly diverge from the basic models or the pictures set by the UHV measurements.