This paper documents a structural property of AI search recommendation that we term the Persona Reversal: the brand that ChatGPT's AI search recommends most strongly changes when the audience persona shifts, even when the prompt and model are held constant. Using 3,052 brand-level and 8,811 prompt-level unpersonalized API observations across 30 brands in 4 industries from January through May 2026, we measure intra-brand Persona AiRR Drift (PAD) of up to 40.40 AiRR Score points in a single persona shift, with proportional PAD values reaching 152.8% above a brand's overall baseline. We find that aggregate AI visibility scores systematically misrepresent the recommendation behavior brands actually face from their target customers. The implication for marketing measurement, brand strategy, Generative Engine Optimization (GEO), and Answer Engine Optimization (AEO) is that the unit of analysis must change. AI search visibility is not a brand property. It is a property of the brand-prompt-persona triple.