Kino wasn't educated, and thus, couldn't challenge the doctor's prognosis for his son. He was stuck because he couldn't make a mistake..... he felt that his ignorance exposed his family to danger.
He did not know, and perhaps this doctor did. And he could not take the chance of putting his certain ignorance against this man's possible knowledge. He was trapped as his people were always trapped, and would be until, as he had said, they could be sure that the things in the books were really in the books. He could not take a chance- not with the life or with the straightness of Coyotito.