There are items that people use as media of exchange themselves, like Federal Reserve Notes, bitcoins, and so on. And then there are items that people use as media of exchange that are redemption claims to money, like checkable deposits, passbook saving accounts, and so on.
The evidence that money substitutes require redemption as a condition of their continuing use as a medium of exchange is the fact of continuing redemption by the issuer of the money substitute. Banks could quit offering on-demand, at-par redemption for their checking accounts, etc. and, faced with such a prospect, people at large may or may not continue to accept such account balances in lieu of accepting money or money substitutes issued by non-bank institutions, but the fact of continuing redemption makes these deposits money substitutes and not money itself.
A money substitute has an objective definition that depends only on the fact of redemption and not on how people subjectively value the item. Whether or not people use some particular item as money or a money substitute depends on their subjective valuations, but the categories of money and money substitutes do not. They are definitions.