Earlier quoted context omitted.
Who is lying in this case? Banks are one, if not the most, regulated companies in the US. What are banks lying about and who are they lying to? I'd assume the government would come down on them pretty hard if it turns out that all banks are lying to their customers as federal and state regulations on banks are pretty heavy handed to make sure that the vast majority of banks are healthy at any given time.
The bank is telling two or more people they own (or, at least, have access to) the same dollar at the same point in time. With duration matching you can have loans, but it is clear that depositor A can't get dollar X back until time point T, and that borrower B can have the dollar until then.
But they don't do that. Or, I've literally never seen them do that.
What the bank tells me is what my current deposit is. That's the truth. They aren't representing that the amount they're listing is a specific dollar somewhere, they're telling me how much money I've given to them.