If the provider says "the model will always be right or your money back" then the provider has got responsibility. If there's no guarantee, there's no responsibility on their part, just on the person whose job it is to try and solve a problem with the model.
If you give an "intelligent agent" offered by one of these model providers a task of updating the content of your website, and it updates it with inappropriate adult content, who incurs the cost of the machine's error? The model provider generally does not.
It it makes a mistake and deletes your website from AWS, who is responsible?
If it targets another website because it decides that it is "part" of your website and attempts to break into it, who is responsible?
Something in your prompt led it to do that, is alex0015's point. The statistical odds of these frontier models screwing up to that extent are so impossibly low that it would almost have to be intentional or accidental negligence on the part of the prompt writer to accidentally have their agent write pornography to their website.
The burden of the mistake would have to fall on the person that gave the tool instructions, because it can't know that what it did was wrong. Wrong is subjective in this case. It only did what it did because you, figuratively speaking, encouraged it to.
In general, the person whose job it is to provide the company with a working, non-adult website and not hack into other websites is the one who would receive consequences for failing to meet those expectations.
These tools can push out more results than a human can hope to evaluate in a business-sensitive, or even realistic, amount of time. You have to take it at its word that it did things right, and there's no real fear of failure or consequence on the behalf of the agent.