Proverbs 16:10 says, "The lips of a king speak as an oracle, and his mouth should not betray justice." (NIV)
That verse doesn't say the king IS an oracle or that the words he utters always are true or infallible. It says he speaks AS an oracle—with the force and authority of an oracle, but it goes on to say that because of this, the king's mouth should not betray justice.
In saying that the king's mouth 'should not' betray justice, the verse presupposes that even though his speech carries authority, the king still has the capacity to say things that are wrong, untrue, or contrary to the duties and responsibilities of his office.
Rulers occupy a special place, a special office. That office gives them positional authority and power—authority and power derived solely from the office they hold. Because of that, they must control their tongue, self-edit their extemporaneous comments, and guard the language of their formal statements, lest they betray the moral imperative of their office and incur judgement because of it, rather than blessing.