It actually works the same as on google. As in, ChatGPT will happily give you a link to a site with the lyrics without issue (regardless whether the third party site provider has any rights or not). But in the search/chat itself, you can only see snippets or small sections, not the entire text.

1. chatgpt is the publisher, Google is a search engine, links to publishers.

2. LLMs typically don't produce content verbatim. Some LLMs do provide references but it remains a pasta of sentences worded differently.

You are asking for gpt to publish verbatim content which may be copyrighted, it would be deemed infringement since non verbatim is already crossing the line.