"Trust me." implies there is a shared purpose and that both parties are committed to serving that purpose. Essentially, the message is:
1. I can do this.
2. If I need your help, I am prepared to ask.
3. Let me try it on my own first.
4. The vision of success we share will be well served by my decisions and actions.
5. Give me a chance to be independent.
On the other hand, "Leave me alone." is a statement born out of frustration, conflict, and the need to serve oneself. Sure, sometimes we need some "me time" to recharge the batteries, but that is not what I am talking about in this post. What I am describing is a message of isolation, not independence.
The message behind, "Leave me alone." is:
1. What I want to do is more important than what we need to do.
2. I don't want anyone observing my work. (It is harder to take shortcuts)
3. Alone, I am only accountable to me. I don't want to be accountable to anyone else.
4. I am not interested in learning anything new, which might happen as part of a team.
As I imply above, independence is not the same as isolation. The strength of an independent faculty, student, school, teacher, etc. is the ability to apply one's talents in a manner that advances a shared vision of success and purpose. In isolation, the only purpose being served is the individual's.
Trust is an element found in heathy independent environments. Isolation breeds loneliness.