It's clearly not all debts. I actually can't think of any debts this applies to. Your student loan, credit card, auto loan, home loan, water bill, power bill, heck even rent if you're in a modern corporately owned complex... would never under any circumstances accept cash payment. It would be stunning if one even provided an address that isn't a PO box, let alone an address where you could get in the front door if you showed up in person, assuming you were willing to travel a few thousand miles.

At most there might be something like a retail bank branch where you could deposit cash and then request an electronic transmission of the same amount of money.