If you interpret “interpolate” in the literal sense, and apply it to the mechanisms behind LLMs, then the claim that they only interpolate, is straightforwardly false.
Taking it instead as a metaphorical claim may be more valid, but in that case it doesn’t depend on our understanding of how LLMs work.
LLMs are statistical models by construction, so depending on how liberal you want to be with terminology, "interpolate" is not so bad. Might make a statistician upset.
But people aren’t giving a (less literal) definition of what they mean by “interpolate” that relies on the internal mechanisms of these models, just a vague metaphor, which, as this vague metaphor, there’s nothing it uses about LLMs that makes the question “do LLMs just interpolate” less of a type error than “do people just interpolate”.
They’re also capable of performing arbitrary computation when ran in a loop - so they can be made to quite literally interpolate whatever. Philosophers are quite upset, too.
Taking it instead as a metaphorical claim may be more valid, but in that case it doesn’t depend on our understanding of how LLMs work.