That's an interesting way to look at trust but it's highly dependent on your own internal thought process and phrasing.

"I trust he WON'T let go of the ladder."

That's the same as

"I trust he WILL keep the ladder secured."

I'd say trust isn't about what you think the person won't do. It's about the person living up to their word or implied contract. It can be phrased either as a will do or a won't do.

Ladder guy holding it implies he will hold it securely. Doctor with private info implies he WON'T share it irresponsibly. That could also be worded as an expectation that he WILL keep it private.

"I trust Bruce Schneier to not sacrifice his own principles and belief system in backdooring some code or otherwise compromising his work."

OR

"I trust Bruce Schneier to be true to his principles and belief systems and maintain the integrity of his work."