Because she is really trusted? If they give a 16 year old a responsibility that is big, they are doing it for a reason, and that is because they trust that she can take it.
More information in the question? People shouldn't be given responsibility if they can't be trusted with it. So trust should be proven before responsibility is given.
It is better to say, "a 16 year old who is will to have responsibility and show it should be trusted."