I don't think the author was under the impression that banks physically store money. They meant the digital currency does not sit idle on the bank's asset list. They're just using normal human language.
The deposits aren't assets to the bank, they are liabilities. The loans are their assets (your liability is their asset). They don't need to "do anything" with your deposit because it doesn't exist. If I increment the number 2 to the number 4, have I brought something into existence, in particular 2 "things"? What is that? Why can't I just bring 3 things into existence without incrementing the initial number?
If this sounds silly it's because it is. I thoroughly recommend anyone who is confused to a) do their own accounts and b) invent a silly currency inside your accounts and start a bank for your imaginary friends. Just add trust and government support to your bank and you'll be like any other bank.
> They don't need to "do anything" with your deposit because it doesn't exist.
Uhm yeah they do. If they take my money and then just do nothing with it then they won't make any money from it. Banks invest your money.
(I don't think that's the main way they make money - it's probably mostly from credit card interest, but they definitely do it.)
The money you pay into banks absolutely exists in every sense.
Banks can create money when they issue loans, which I suppose you could argue doesn't exist. But they aren't allowed to create unlimited money. I'd say it exists as much as any other money exists.
You're wrong, but you're far from alone. Essentially the way the whole finance industry works is there is an enormous gulf between their understanding of money and the general public's understanding. They don't contribute anywhere near as much to society as people think, in fact they fuck a lot of things up, but they run the books, of course they'll come out on top.