We argue that soundness remains essential for LLM-driven static analysis and discuss hallucination-resilient approaches in combining LLMs with static analysis that ensure soundness while improving precision. We investigate the use of LLMs in higher-order control-flow analysis, building on the abstracting abstract machine (AAM) framework and delegating abstract address allocation to an LLM. Our analyzer LLMAAM maintains soundness regardless of LLM behavior, while adaptively tuning analysis precision. We report preliminary results and outline broader opportunities for sound LLM-driven analysis.