A typical NLP system for medical fact coding uses multiple layers of supervision involving fact-attributes, relations and coding. Training such a system involves expensive and laborious annotation process involving all layers of the pipeline. In this work, we investigate the feasibility of a shallow medical coding model that trains only on fact annotations, while disregarding fact-attributes and relations, potentially saving considerable annotation time and costs. Our results show that the shallow system, despite using less supervision, is only 1.4% F1 points behind the multi-layered system on Disorders, and contrary to expectation, is able to improve over the latter by about 2.4% F1 points on Procedure facts. Further, our experiments also show that training the shallow system using only sentence-level fact labels with no span information has no negative effect on performance, indicating further cost savings through weak supervision.