If you hack your bank and put some additional zeros to you account you basically counterfeited digital dollars, but no original thing to copy it existed. So given your logic it is impossible to make fake digital money. This is obviously absurd. Fake money is the one that is intrinsically worthless and is put into circulation with the intention to extract real money, goods and services from other people, without providing these people something valuable in the future.
As I said, you don't understand money. If you hack in a bank, you don't create counterfeit dollars.
The dollar is the
physical form for debt. For "I owe you" a certain amount of.. things.
When the banks will show you a number in the account, that's not dollars, since it's not physical. That's simply "the bank owes you this amount". Completely different thing! That's why for every dollar you deposit, they can lend .. how many? 6, 8? Because it's only a promise, not money.
When you pay with the card, you "transact" the same "I owe you" in the digital form. It's not (physical) dollars.
And when you hack in, you trick the bank to think they owe you back more than you deposited. When you withdraw from ATM, you'll get dollars. And I don't know any ATM the delivers fake dollars.
The dollar is debt, regardless if it is physical or digital. You can counterfeit both by creating bills or digits that are not backed by loan contract or your obligation to reply the debt. Hence, you are using semantics and focus on things irrelevant for this topic.