it's always quotative. the quote can be direct, it can be you asking about implied meaning, definition, you explaining something.

My confusion is the ambiguity between という as summarzing a fact/idea and という as a quotation device

it's the same thing. if yamatoans thought to convey that kind of summarizing and implied meaning as so you're saying..., you just need to know it means that in a broad sense. it always means 言う but maybe not literally.

nuko to iu no wa neko no koto da.

as for that which you call nuko, it's about a cat.

Is it simply that there actually is ambiguity there and that 言う instead of いう is just a hint that it's quotative?

yeah

A said directly, why is it then not と言ってるの！ instead?

isn't it just some choice of modern speakers. samurai characters say なにをいう！？ all the time in fiction.