There's something I don't understand with this, though.

Your private credit is with an issuing lender - which not all are Fed banks, correct? It certainly must be possible to have private credit with a private entity without involving fractional lending (on what?) or other federal 'privilege'. I enter a contract with you, and you tell me you'll pay for up to $10,000 of anything I want, as long as I simply pay you back, including any interest if I haven't squared up with you by the end of each month.

But in any event, it's not like you have "money", even on paper, with a credit card. You're in the hole if you use it. It's not 'income' (IRS definition or otherwise), and you don't ever report it on a return (assuming you're subject to a return, that is).
I'm just having trouble following the logic on how every instance of a 'private credit' would subject you to any sort of income tax. You pay for my things, and I pay you back in lawful money.