다고 오다

come saying or claiming X

-다고 quotes the reason or intention someone arrives with, and 오다 is their coming: 얘기하고 싶다고 오시고 싶다고 'he said he just wanted to come and talk', 이거인 것 같다고 오시는 분들 'patients who come saying they think this is what they have'. It also does a dismissive rhetorical turn — 뭔 얘기를 했다고 와서, roughly 'what have you even done, turning up like this'. The quoted claim belongs to the person arriving, not to the speaker.