Even the Vatican, the smallest country, issued its own coins. Paper money. They use euros. You know, the Vatican is as big as the Forbidden City in Beijing.
What the landlord said may be that some small countries have a high proportion of foreign exchange, a small population and a small area, so they voluntarily gave up the right to issue money and directly used the currency circulating in other countries. But it is definitely not that they have lost the right to issue money.