Trustworthiness is a function of two things — character and competence. Stephen Cover makes this point well in Principle Centered Leadership:
Most people equate trustworthiness with character alone. Character is vital, but it is also insufficient. For example, would you trust a surgeon to perform a critical operation who is honest in his billing practices, but who has not kept up on advances in his field and is professionally obsolete?
On the other side, some people equate trustworthiness with competence alone. That, too, is insufficient. Would you hire a doctor who was up on the advances in his field but not honest in his billing practices?
And we need to go beyond simply the minimum character requirements. We should seek to be people of character who pursue the good of others. And, we should seek to be incredibly competent in this, because there are few things worse than well-intentioned incompetence.
Pursue both character and competence.