You're overthinking it.

When you sign a BTC transaction, from the point of view of a normie, you're doing exactly the same - authorize the "custodian", which is "the network", to release the funds. Just as with the credit card. That's trivial and familiar. 

People have trouble with BTC because of the "not backed by anything" part, indeed. Because they truly believe fiat is "backed" by the government,  by taxes, by law, or even by gold, and that it is actually there in the bank, physically sitting in a box.