As a US citizen there are only a handful of countries/territories that you can work legally without any sort of paperwork (Puerto Rico, USVI, Samoa) and a handful more that have official working holiday schemes:
- Singapore
- New Zealand
- Australia
- South Korea
- Ireland
If you are in the EU citizen you can work freely within the EU.
However most folks aren't writing about working holiday visas or working within the EU. They are writing about South East Asia and Central/South America. Neither of which allow people to go and work without permits.
People are breaking the law and being way too public about it.