When Vision-Language Models (VLMs) answer correctly, do they rely on the image? We introduce a Tri-Layer Diagnostic Framework that asks three questions of every (image, question) pair when the image is blanked: does the model register that the image is missing (Latent Anomaly Detection, LAD), does its output distribution depend on the image (Visual Necessity Score, VNS), and does it nonetheless commit to a content answer? The cascade assigns each pair of any existing benchmark to one of four modes: Perceptual Blindness, Language Shortcut, Visual Sycophancy (the blank image registers and matters, yet the model commits to a fabricated answer), or Robust Refusal. Across nine open-weight VLMs and 9,000 model-sample pairs, 28.1% are Visual Sycophancy, 18.6% Language Shortcut, 5.6% Perceptual Blindness, and 47.8% Robust Refusal. The modes are strongly model-specific: the Qwen3-VL models refuse on blank input in 93-98% of pairs, whereas Pixtral-12B commits to an answer in 72%. Within-generation scaling increases Visual Sycophancy in both Qwen2.5-VL (7B->72B: 25.5->40.1%) and Llama-3.2-Vision (11B->90B: 34.3->48.0%), while the newer Qwen3-VL generation nearly eliminates it. A blinded human study confirms that LAD and VNS track what annotators observe, and that 80% of Visual-Sycophancy responses carry no textual sign that the image was blank.

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