It's like a genotype/phenotype distinction, the genotype may be statistical text generator but the phenotype is something much more.

Not parent but I think you're being rather dense. They are _obviously_ statistical text generators. There's plenty of source code out there, anyone can go and inspect it and see for themselves so disputing that is akin to disputing the details of basic arithmetic.

But it is no longer useful to bring that fact up when conversing about their capabilities. Saying "well it's a statistical text generator so ..." is approximately as useful as saying "well it's made of atoms so ...". There are probably some very niche circumstances under which statements of each of those forms is useful but by and large they are not and you can safely ignore anyone who utters them.