> That entity would be whoever owns those US dollar printing presses that are printing the dollars right now.

Except that most "dollars", or any currency for that matter, are not physical but rather digital values in a computer some place.

The modern "printing press" is a computer located at the central bank of the currency in question (Fed, ECB, etc).

(Technically most money is actually created by private banks through loans and entries in banks' ledgers.)