Savings can come in many forms. It does not have to come in the form of between a bank and you. Yet, what you stated is not true. It is true in the Keyensian driven system we have now. There was a time in the past where banks could not loan out more than they could back. Thus you keeping a bank note was not the same as keeping a debt driven bank note that is effectively a form of I.O.U. towards money that the bank loaned out without having assets to back it.
What you say is true if the monetary system is fiat. If it is not backed by anything then every note you hold is actually debt.
If it is backed by something then that is not true. So because a thing is one way now does not mean it needs to remain that way, or that it has always been that way.
Yet that is besides the point. That DOES directly address what you are talking about.
It does not address what my article is about. If you and I incur debt beyond our means to operate, we have to be responsible, make cuts, balances, etc.
The government is supposed to do this as well. Instead they use fear and emotions to convince people to instead let them raise their credit card limit.
This is irresponsible and regardless of your views on debt vs savings it is a big problem. That is what my article is about.
I cannot see a way to spin how the government does these things as a positive.