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.
About 'fiat' from Bitcoin: This project started as a counterbalance to the forthcoming cashless society. Hard cash have some unique features like anonymity and freedom.
You don't have to use Bitcoin as value. In a community you could use other commodities as well if you have your own dedicated server. But in a public solution as I'm currently running, Bitcoin is the natural choice. At the moment I'm giving away one free ticket per user. These tickets don't have value at first but I can assign value to tickets as mentioned here https://52blocks.net/ivalue52.html . And as mentioned to Eugenar , I'm currently using the Lazy API model. By using the ticket verify code you will see it's value (in the future).
1-3: In the future, everyone can purchase tickets. But you need to pay to a given BTC address to give it value. In a fully public solution there can be several tickets with no value, but the ticket you use for transaction can be verified. So a person can receive a ticket holding value and trade it for bitcoin. But if these tickets are used as complementary currency, you don't need to trade for bitcoin on every transaction as long as there is trust. In a trustless environment you can 'burn' a ticket for each transaction.
These tickets have several features not mentioned to prevent "counterfeit".