Yep. That is how the system works. Can't disagree really. A couple of points:
John Titus (has a website and video series called BestEvidence) was on the Unlimited Hangout podcast a while back and made a really interesting point (which I think you're making too):
If you have coins, that's money. If you have cash .. well it's a note, but you can still fudge and say that's money. It's a store of value. Once you put $1,000 in a bank, it's no longer money. The bank gives you a credit. Liabilities and assets get adjusted on their balance sheet. You have $1,000 in credit, but it's no longer legal tender. We don't think about it because a bank always honors that credit to other banks .. but it's not really money. If the bank collapses, in the US you depend on FDIC that insures up to a certain amount of the bank's holding to the depositor.
The other major thing is that the 2020s money era printing was really really unique. Through some laws, the Federal Reserve was able to swap for real actual assets. Normally the Federal Reserve can't hold a building or a factory on their books. All they have are reserves, not money. Who the fuck is going to trade their assets for reserves except for banks? But through some new laws and tricks and using first party lenders, the Fed does have reserves traded for assets now, and that is what caused trillions of new money to be added to the consumer money supply. In 2008, the books were just shifted between banks. People (who weren't losing their houses) didn't see it. But 2020 inflation is way different. I can't explain it as well as him, but it's super interesting: