Globally, disparities in healthcare infrastructure remain stark, leaving countless communities without access to even basic services. Traditional infrastructure planning is often slow and inaccessible, and although many architects are actively delivering humanitarian and aid-driven hospital projects worldwide, these vital efforts still fall far short of the sheer scale and urgency of demand. This paper introduces MedBuild AI, a hybrid-intelligence framework that integrates large language models (LLMs) with deterministic expert systems to rebalance the early design and conceptual planning stages. As a web-based platform, it enables any region with satellite internet access to obtain guidance on modular, low-tech, low-cost medical building designs. The system operates through three agents: the first gathers local health intelligence via conversational interaction; the second translates this input into an architectural functional program through rule-based computation; and the third generates layouts and 3D models. By embedding computational negotiation into the design process, MedBuild AI fosters a reciprocal, inclusive, and equitable approach to healthcare planning, empowering communities and redefining agency in global healthcare architecture.