Just as shovels, seeds and garden tools are backs. All have uses beyond mere trade tokens or accounting records.
If you were to wash-up on a deserted island with the debris of the ship wreck and felt certain that rescue was unlikely, you would be wasting your time looking for all the bit coins. So federal bills, in that they might be useful in starting a fire or wiping one's butt, would be more valuable. The ink pattern on those bills would have nothing to do with their actual value though.
Mighty mountains in grandeur stand, but tiny raindrops turn them to sand! Noah, I think I just felt a raindrop!!