Translation:I don't know why they don't trust him.
Εμπιστεύομαι means to trust someone and it only works with this structure, it does not have an alternative voice form. Therefore, to be trusted by someone is (το) να με/σε/τον εμπιστεύεται κάποιος. Which is Κάποιος με/σε/τον εμπιστεύεται or Κάποιος εμπιστεύεται εμένα/εσένα/αυτόν, i.e. the original subject-verb-object structure. (I think that was the question?)