I would say it's the opposite: fiat is based on trust, in other words perhaps intimidation, that's why some countries can print money with little negative effect. The future of cryptocurrency will be its trustless systems.
You are correct. It is the fiat money (like the US Dollar and any other paper currency) that is basing too much on trust...trust that the government issuing the paper notes can be good in managing the economy of the country that can somehow affect the value of its issued money.
Now, Satoshi understand human nature more than we do and he knew that trust can be scarce in the real world and so we have the blockchain technology that can facilitate transactions even with people who don't trust each other that much for many factors.
This is actually one of the most important essence of cryptocurrency as built by that great figure named Satoshi Nakamoto. Brilliance is one word to describe what the 'man' contributed for the humanity on this modern age we are in right now.