When a currency is not anyone else´s liability (gold, silver, bitcoin), it is non sense to talk about confidence, the same way it is nonsense to talk about confidence in bread, wheat or oil. What the market takes in consideration is their properties to assess their utility. In the case of gold or bitcoin, the market would consider its properties as medium of exchange (easy to transport, divisible, easy to identify, hard to fake, relatively scarce, etc).
By the way, the huge difference between bitcoin and commodity based currencies such as gold or silver is that Bitcoin is much easier to transport.
Only when a currency is based on credit, then confidence is important. The fact that a currency is not reedeemable doesn´t mean it is not credit.
Fiat currencies are credit because the issuer obligues itself to accept it. How much would the dollar last if the Federal Reserve or commercial banks refuse to accept dollars to cancel debts and instead require gold to its debtors?
The obligation to redeem a currency for a specific economic good is not the only kind of obligation, there is also the obligation to accept it to cancel debts.
There is a very good reason that fiat currencies are registered as liabilities at banks and central banks balance sheets, because there is not doubt they represent an obligation for them.
For fiat currencies, the market has to assess as far as possible the asset column of the bank´s balance sheets that do back their liabilities (the fiat currency they issue). What´s in that asset column?: Mainly corporate and government bonds, mortgages, business loans, student loans, MBSs, derivatives, etc. That is, a miriad of third party obligations, again. But you know, Bitcoin is the one that is very complex….