In collaborative dialogue, shared perception does not guarantee shared interpretation. Mutual understanding must be established through interaction. We investigate whether vision-language models (VLMs) can distinguish what could be shared from what has been shared between dialogue participants through grounding. We formulate this as an interpretation-matching task on 13,077 annotated reference expressions from HCRC MapTask dialogues, and evaluate VLMs under systematically controlled manipulations of dialogue context and map-information access. Our results show that providing authentic map images improves overall performance but shifts models toward over-predicting alignment. Textual descriptions of the same map content reproduce this bias, while non-informative images suppress alignment predictions entirely, indicating that the bias is driven by task-relevant map content, not the visual channel. This improvement comes at the cost of degraded accuracy on non-aligned cases. Calibration analysis and reference-chain tracking further suggest that models rely on static referential cues on the maps rather than tracking how grounding unfolds through dialogue history. We observe these patterns most clearly in Qwen3-VL-8B-Instruct and, to varying degrees, in four additional models from two architecture families. In models that exhibit the bias, map content, whether presented visually or textually, is treated as evidence of mutual understanding, conflating potential with established common ground.