That the data set aggregator doesn't directly host the images themselves matters when you want to issue a takedown (targeting the original image host might be more effective) but for the question "Does that mean a model was trained on my images?" it's immaterial.
* Assuming the users regularly check the images are still being hosted (probably something that should be regulated)
As with almost any URL, it is not in and of itself an image.
As an aside, this presents a problem for researchers because the links can resolve to different resources, or no resource at all, depending on when they are accessed.
Therefore this is not a static dataset on which a machine learning model can be trained in a guaranteed reproducible fashion.
The issue in question is that many/most large generative AI models were trained with personal data.