I think the issue is much more complicated than simply not trusting anyone! IF YOU PORTRAY ‘ NO TRUST’ to all your business partners, employees, customers, etc., without taking the proper measures, you will likely make everyone want to commit fraud and prove you right, in your working environment! The desire for security is a key subconscious motivator in developing trusting relationships in an any organization.
Let us not forget that as Aristotle (384-322 BC), writing in the Rhetoric, suggested that Ethos, the Trust of a speaker by the listener, was based on the listener's perception of three characteristics of the speaker: the intelligence of the speaker (correctness of opinions, or competence), the character of the speaker (reliability - a competence factor, and honesty - a measure of intentions), and the goodwill of the speaker (fri3ndship, favorable intentions towards the listener).
Furthermore, my opinion is that you do need a friendly and trustworthy working environment but it should be complemented by a Corporate Controls Framework with control mechanisms at five levels: