Perhaps this is tangential, but if we're assuming non-omniscient perspectives then what allows you to conclude that the only way to be trusted absolutely is to never be observed to have lied?

If the supervisors weigh positive evidence over negative evidence, a very common bias, then we should actually expect them to trust you more if they have accumulated a great deal of reliable evidence of when you do lie. That's one reason being caught in an understandable lie is a way con artists can build trust.

It seems that you're using honesty as a behavior, truth as a value of a statement or a communication, and trust as a feature of a relationship as though they are interchangeable. But they really aren't.

Even if you wish to behave in such a way to communicate things as accurately as possible (honesty) it becomes necessary to say things which are not accurate in themselves (lie), in order that the outcome of communication is accurate (honest).