That's not what fungibility is. Fungibility is the ability to replace the object (in this case the money itself) with an equivalent object (in this case another bill of the same value) and they can be used interchangeably.

Using the bread example: The baker in NYC doesn't care if you use a $20 bill from 1980 or a brand new one from the bank. Also, the baker in Orlando doesn't care which particular bill you use either, so long as its legal. That is fungibility. Money is designed (in the US at least) to be perfectly fungible, and that is a great feature of it.