This paper contributes to the nascent debate around safety cases for frontier AI systems. Safety cases are structured, defensible arguments that a system is acceptably safe to deploy in a given context. Historically, they have been used in safety-critical industries, such as aerospace, nuclear or automotive. As a result, safety cases for frontier AI have risen in prominence, both in the safety policies of leading frontier developers and in international research agendas proposed by leaders in generative AI, such as the Singapore Consensus on Global AI Safety Research Priorities and the International AI Safety Report. This paper appraises this work. We note that research conducted within the alignment community which draws explicitly on lessons from the assurance community has significant limitations. We therefore aim to rethink existing approaches to alignment safety cases. We offer lessons from existing methodologies within safety assurance and outline the limitations involved in the alignment community's current approach. Building on this foundation, we present a case study for a safety case focused on Deceptive Alignment and CBRN capabilities, drawing on existing, theoretical safety case "sketches" created by the alignment safety case community. Overall, we contribute holistic insights from the field of safety assurance via rigorous theory and methodologies that have been applied in safety-critical contexts. We do so in order to create a better foundational framework for robust, defensible and useful safety case methodologies which can help to assure the safety of frontier AI systems.