backing implies a promise to be able to redeem the unit of currency for something else
In a wisdom-of-crowds system, the promise comes from faith that somebody in the future will still find bitcoins valuable, and be willing to give you something in return.
True, it isn't a promise from one particular institution or person to redeem for one particular something else, so it doesn't fit your definition of 'backing.' But I trust The Crowd more than I trust any one particular institution (especially institutions like governments, who have a long history of breaking promises).
See my recent "Is store of value enough?" blog post for more thoughts along these lines.