At inference time, there's a whole new legal question: are the specific outputs of the model substantially similar to anything that the LLM had access to? Even if AI training itself was infringement, a specific generated output of that model could be noninfringing anyway. And vice versa, AI training being fair use doesn't form a blanket defense against a specific AI copyright infringement. If you ask the model to create an art program, it could still generate something substantially similar to the code of an existing art program.
In the case of regurgitation[0], the fact that an LLM was involved is immaterial. The only thing the law cares about is if a copy was made somewhere along the chain and if the alleged copy was substantially similar to the purported original. The only thing LLMs do for this analysis is make access to the original far easier to allege, because LLMs are trained on everything.
[0] Inclusive of both model weights and context regurgitation
Lovable have the following terms, for example - "You assume full responsibility for your use of AI Output and agree not to rely on it for critical or high-risk functions (including medical, legal, financial, or safety-related purposes) without appropriate safeguards. AI Output may be similar or identical to content generated for other users who submit similar prompts. We do not guarantee that AI Output will be unique, free of third-party rights, accurate, suitable for any particular purpose, or that it will build, repair, complete, or improve any application or project or achieve any particular result."