The standard definition of a fiat currency is that it’s not backed by some kind of asset and thus has only the value given by social convention. The most widespread examples are backed by sovereign states and thus have the weight you describe but there have been private ones as well.

This is why I described it as a very weak one because it doesn’t even have the commitment of a bank behind it and the extremely highly operating costs means there’s a real long-term risk of not being able to find a buyer.