It’s not stored as the full material though. If a human that can sing a copyrighted song is not considered to have a recording of the copyrighted song in their brain, so too are LLMs able to spit out their training data without having to store them.
How do you know what it’s storing? I certainly don’t, but I know what the security researchers have found that proved it was storing copyrighted material and real people’s private info or PII.
You being able to spit people’s name and personal details doesn’t mean you are keeping a database of those details in your brain. It’s all just neurons and the connection between them that can be triggered to extract those details out.
LLMs also attempt to mimic this method of not storing direct information, but tweaking parameters to ‘learn’ the information. Inside LLMs are just a bunch of parameters that if not well-designed, can be made to spit out what they have learnt. That doesn’t mean they store those information as is.