To some extent, and obviously grossly over-simplified here, copyright is the act of taking some already public good and putting private rights on it. My reading of the amicus is that the government is arguing that particular rights that NY Times are asserting that they have are not ones that promote the aims of the original reasons for copyright to exist and so aren't necessarily ones which need to govern the behavior of any other people (in this case OpenAI, but this likely applies to any LLM training no matter the size).