Vision-language models (VLMs) are impactful in part because they can be applied to a variety of visual understanding tasks in a zero-shot fashion, without any fine-tuning. We study $\textit{generative VLMs}$generative VLMs that are trained for next-word generation given an image. We explore their zero-shot performance on the illustrative task of image-text retrieval across 8 popular vision-language benchmarks. Our first observation is that they can be repurposed for discriminative tasks (such as image-text retrieval) by simply computing the match score of generating a particular text string given an image. We call this probabilistic score the $\textit{Visual Generative Pre-Training Score}$Visual Generative Pre-Training Score (VisualGPTScore). While the VisualGPTScore produces near-perfect accuracy on some retrieval benchmarks, it yields poor accuracy on others. We analyze this behavior through a probabilistic lens, pointing out that some benchmarks inadvertently capture unnatural language distributions by creating adversarial but unlikely text captions. In fact, we demonstrate that even a "blind" language model that ignores any image evidence can sometimes outperform all prior art, reminiscent of similar challenges faced by the visual-question answering (VQA) community many years ago. We derive a probabilistic post-processing scheme that controls for the amount of linguistic bias in generative VLMs at test time without having to retrain or fine-tune the model. We show that the VisualGPTScore, when appropriately debiased, is a strong zero-shot baseline for vision-language understanding, oftentimes producing state-of-the-art accuracy.