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Vision-language models trained on large, randomly collected data had significant impact in many areas since they appeared. But as they show great performance in various fields, such as image-text-retrieval, their inner workings are still not fully understood. The current work analyses the true zero-shot capabilities of those models. We start from the analysis of the training corpus assessing to what extent (and which of) the test classes are really zero-shot and how this correlates with individual classes performance. We follow up with the analysis of the attribute-based zero-shot learning capabilities of these models, evaluating how well this classical zero-shot notion emerges from large-scale webly supervision. We leverage the recently released LAION400M data corpus as well as the publicly available pretrained models of CLIP, OpenCLIP, and FLAVA, evaluating the attribute-based zero-shot capabilities on CUB and AWA2 benchmarks. Our analysis shows that: (i) most of the classes in popular zero-shot benchmarks are observed (a lot) during pre-training; (ii) zero-shot performance mainly comes out of models' capability of recognizing class labels, whenever they are present in the text, and a significantly lower performing capability of attribute-based zeroshot learning is only observed when class labels are not used; (iii) the number of the attributes used can have a significant effect on performance, and can easily cause a significant performance decrease.