The integration of path reasoning with language modeling in recommender systems has shown promise for enhancing explainability but often struggles with the authenticity of the explanations provided. Traditional models modify their architecture to produce entities and relations alternately--for example, employing separate heads for each in the model--which does not ensure the authenticity of paths reflective of actual Knowledge Graph (KG) connections. This misalignment can lead to user distrust due to the generation of corrupted paths. Addressing this, we introduce PEARLM (Path-based Explainable-Accurate Recommender based on Language Modelling), which innovates with a Knowledge Graph Constraint Decoding (KGCD) mechanism. This mechanism ensures zero incidence of corrupted paths by enforcing adherence to valid KG connections at the decoding level, agnostic of the underlying model architecture. By integrating direct token embedding learning from KG paths, PEARLM not only guarantees the generation of plausible and verifiable explanations but also highly enhances recommendation accuracy. We validate the effectiveness of our approach through a rigorous empirical assessment, employing a newly proposed metric that quantifies the integrity of explanation paths. Our results demonstrate a significant improvement over existing methods, effectively eliminating the generation of inaccurate paths and advancing the state-of-the-art in explainable recommender systems.