If that software happens to output an image that is in violation of copyright then it is not the fault of the model. Also, if you ran this software in your home and did nothing with the image, then there's no violation of copyright either. It only becomes an issue when you choose to publish the image.
The key part of copyright is when someone publishes an image as their own. That they copy an image doesn't matter at all. It's what they DO with the image that matters!
The courts will most likely make a similar distinction between the model, the outputs of the model, and when an individual publishes the outputs of the model. This would be that the copyright violation occurs when an individual publishes an image.
Now, if tools like Stable Diffusion are constantly putting users at risk of unknowingly violating copyrights then this tool becomes less appealing. In this case it would make commercial sense to help users know when they are in violation of copyright. It would also make sense to update our copyright catalogues to facilitate these kinds of fingerprints.