The description of how LLMs process text is correct. I agree with your summary, Hanno.
The fact remains, though, that LLMs are often successful at mimicking human language. That is at the crux of why LLMs are perceived as “intelligent”.
<aside> It’s also fodder for science fiction when characters are puzzled by whether some other entity is intelligent. </aside>
Intelligence requires self-awareness, a quality LLMs surely do not possess.