Various green building rating systems (GBRSs) have been proposed to reduce the environmental impact of buildings. However, these GBRSs, such as Leadership in Energy and Environmental Design (LEED) v4, are primarily oriented toward a building’s use stage energy consumption. Their application in contexts involving a high share of renewable energy, and hence a low-impact electricity mix, can result in undesirable side effects. This paper aims to investigate such effects, based on an existing office building in Quebec (Canada), where more than 95% of the electricity consumption mix is renewable. This paper compares the material impacts from a low-energy context building to material considerations in LEED v4. In addition to their contributions to the building impacts, material impacts are also defined by their potential to change impacts with different material configurations. Life cycle assessment (LCA) impacts were evaluated using Simapro 8.2, the ecoinvent 3.1 database, and the IMPACT 2002+ method. The building LCA results indicated higher environmental impact contributions from materials (>50%) compared to those from energy consumption. This is in contrast with the LEED v4 rating system, as it did not seem to be as effective in capturing such effects. The conclusions drawn from this work will help stakeholders from the buildings sector to have a better understanding of building environmental profiles, and the limitations of LEED v4 in contexts involving a low-impact energy mix. In addition, this critical assessment can be used to further improve the LEED certification system.