Verifier Choice is a Benchmark Design Variable: Auditing Structural Counting Evaluation in Text-to-Image Models

Automatic evaluation is now central to text-to-image benchmarking, but the verifier that converts generated images into scores is often treated as an implementation detail. We argue that this is unsafe: an automatic benchmark score is a property of the image generator, prompt distribution, verifier, verifier-use protocol, and scoring rule, not of the generator alone. We study this issue in structural counting, a controlled setting where human-visible counts can be audited. We construct a verifier-centric audit suite over seven counting objects: cell phones, chairs, and traffic lights for object counting, and clover leaflets, dresser drawer fronts, power-strip sockets, and turbine blades for substructure counting. Across 6,240 generated images from Qwen-Image-2512 and FLUX.2-dev, we compare open MLLM verifiers under count-only, reject-aware, zero-shot and few-shot protocols, plus TIFA-like target queries, a detector baseline, and frontier closed-model checks on two hard objects. On a balanced 2,280-image evaluation split, aggregate score matching can coexist with image-level disagreement, and verifier-use protocols and generator distributions change the measured reliability. Every verifier-protocol configuration also shrinks the human score difference between the two generators, by 7.5-25.0 pp, and with a third generator, Z-Image, all four tested protocols reverse the human ordering of Z-Image and FLUX.2-dev on our fixed prompt suite. GPT-5.5 and Claude Opus 4.7 checks do not remove the failure modes: GPT-5.5 still has only 59.92% clover valid-count fidelity, while Claude Opus 4.7 has lower same-slice agreement ($κ=0.432$). We propose reporting automatic benchmark scores with a factorized verifier reliability profile: aggregate score gap, image-level agreement, generator-comparison distortion, valid-image count fidelity, rejection behavior, output compliance, and directional bias.