I'm working on an idea and it might sound a bit far-fetched but it is a 'virtual currency' made to be stored offline much like a paper wallet. But I'm not storing any bitcoin private key. I'm creating what is called a ticket. Each ticket has a unique set of codes and the whole idea is that it must be easy for people to write down these codes so you can create your own set of money or complementary currency. A long story short, my plan is to use Bitcoin as an "intrinsic value". Since the whole point of this project is mimicking physical cash in a cashless society 
it can't be backed by fiat.
it can't be backed by fiat. CMIIW, but this sounds like making a 'fiat' from Bitcoin, isn't it? I'm still not sure about the ticket that you're talking about but,
1. Who's gonna guarantee that there's a real Bitcoin backing those tickets?
2. Who can create those tickets?
3. How to verify them?
As you said, it relies on trust, but there must be a way for you to check if fraud ever happens. Don't assume that everyone is good people. Instead, assume that they'll cheat all the way.