If you owe the bank $100, that's your problem. If you owe the bank $1.7 billion, that's the bank's problem.
This joke only works if you actually impose a cost on AWS of 1.7 billion. If they just serve you a bill for no reason, it's still your problem.
Next question we'll find out is what if you owe the bank $1.7 trillion?
I saw this in action on a smaller scale. In a past job, my wife organized events for a decent sized company. After an event, she'd typically have a $300k+ balance on her corporate Amex. When she went on maternity leave, the person filling in for her job neglected to actually pay the bills, so when she returned there were quite a few emails and voicemails from Amex regarding the over $500k balance.
The messages started as polite and eventually started to get more desperate in tone. At no point were they threatening or adversarial.