"Trust men and they will be true to you; treat them greatly, and they will show themselves great." -- Ralph Waldo Emerson
Every organization needs trust. Without it, people can feel invalidated and become resentful.
From a counterintuitive perspective, trust is always accompanied by mistrust. They come in pairs whether you like it or not. Therefore, if you want to eliminate mistrust, you will have to kill trust. If there is no dependency on trust, people will have to relate to one another as their commitments. By killing trust, people are honored as their word and their actions are always a direct correlate of their words.
As for greatness, I lost both my parents when I was 21. As the oldest of 4 children, I was committed that what was left of the family continued to move forward in a powerful way. One of the ways I did that was to treat my brother and sisters, whose ages were 19, 16 and 12, as though they were truly great. Without question, they accomplished things that you would never expect from someone their age, even though I asked them to do tasks that they had no idea how to do.
While my expectations were for greatness, I guided them through many endeavors until they were successful. This built confidence and allowed me to delegate increasingly complicated tasks to them each passing day. Whether they succeeded or failed in the beginning was irrelevant. It was more important that I was committed to their greatness and took the time to develop it.
As Mr. Emerson states, developing greatness in people will always outperform trust.