It is an algorithm that searches a dataset and when it can’t find something it’ll provide convincing-looking gibberish instead.

This is very misleading. An LLM doesn’t have access to its training dataset in order to “search” it. Producing convincing looking gibberish is what it always does, that’s its only mode of operation. The key is that the gibberish that comes out of today’s models is so convincing that it actually becomes broadly useful.

That also means that no, not everything an LLM produces has to have been in its training dataset, they can absolutely output things that have never been said before. There’s even research showing that LLMs are capable of creating actual internal models of real world concepts, which suggests a deeper kind of understanding than what the “stochastic parrot” moniker wants you to believe.

LLMs do not make decisions.

What do you mean by “decisions”? LLMs constantly make decisions about which token comes next, that’s all they do really. And in doing so, on a higher, emergent level they can make any kind of decision that you ask them to, the only question is how good those decisions are going be, which in turn entirely depends on the training data, how good the model is, and how good your prompt is.