What's the internet backed by? You could argue ICANN but that's not absolutely necessary to have an internet, and in fact other countries want their own version of that.

You could argue "the infrastructure of a bunch of ISP companies", but then you can argue that about Bitcoin as well. The infrastructure of a bunch of (eventually) more trusted companies built around the currency (like Coinbase, etc), and the computing power of the miners propogating the blockchain, plus the entire ledger being public and independently verifiable, could earn the trust of many (it might not, but it could).

There are obstacles getting in the way of that, though, including it being such a new and different concept that most people can't wrap their heads around it.