I noticed to get trusted by people you need to prove you don't need their trust.
That's actually a very good way of looking at it, and a very apt description. Truly, the less trust required of you, the more trustworthy you appear to be. In theory, that is how interactions involving Bitcoin should be considering that Bitcoin is a trustless protocol that relies heavily on transparency and openness. (Although, weirdly enough, people are more cautious online against thieves stealing their measly 0.01 Bitcoin than they are against possible identity thieves and sexual predators.)