Whether you are building healthy relationships in your personal life or at work, honest is important. However, there are some things that don't need to be shared. Your ability to keep important secrets will be vital to this career. Much of the information you are exposed to daily is top secret. The best way you can convince the interviewer of your trustworthiness is by giving an example of your ability to use sound judgement and keep secrets in the past. Think of an important secret you were trusted with. How did you make sure you didn't spill the beans? What was the situation?
"My boss shared with me that he was moving onto another company, before he told anyone else at the firm. It was a lot of pressure for me to know this, but I understood how it would affect his status if I shared this information with anyone else. I respected his wishes and didn't say a word to any of my coworkers."