Extractive models are not always faithful.
A summarization model is always faithful if it uses content from the input documents. Extractive models are a kind of summarization models. Extractive model can only use content from the input documents.
∀x (Model(x) ∧ Summarization(x) ∧ OnlyUseInputDocument(x) → Faithful(x)) ∀x (Model(x) ∧ Extractive(x) → Summarization(x)) ∀x (Model(x) ∧ Extractive(x) → OnlyUseInputDocument(x))