The medical codes prediction problem from clinical notes has received substantial interest in the NLP community, and several recent studies have shown the state-of-the-art (SOTA) code prediction results of full-fledged deep learning-based methods. However, most previous SOTA works based on deep learning are still in early stages in terms of providing textual references and explanations of the predicted codes, despite the fact that this level of explainability of the prediction outcomes is critical to gaining trust from professional medical coders. This raises the important question of how well current explainability methods apply to advanced neural network models such as transformers to predict correct codes and present references in clinical notes that support code prediction. First, we present an explainable Read, Attend, and Code (xRAC) framework and assess two approaches, attention score-based xRAC-ATTN and model-agnostic knowledge-distillation-based xRAC-KD, through simplified but thorough human-grounded evaluations with SOTA transformer-based model, RAC. We find that the supporting evidence text highlighted by xRAC-ATTN is of higher quality than xRAC-KD whereas xRAC-KD has potential advantages in production deployment scenarios. More importantly, we show for the first time that, given the current state of explainability methodologies, using the SOTA medical codes prediction system still requires the expertise and competencies of professional coders, even though its prediction accuracy is superior to that of human coders. This, we believe, is a very meaningful step toward developing explainable and accurate machine learning systems for fully autonomous medical code prediction from clinical notes.