I'm not a statistician, but I have this feeling that this applies primarily when you're testing for simple things from an uniform population - not for a complex factor which has more possible spurious correlations involved than the number of samples you're taking. So I wouldn't have 95% confidence in a result of a politics poll on 1000 people per country.

(Also, there's selection bias involved, including self-selection if the poll was voluntary. I generally don't trust voluntary opt-in polls much, as it's too easy to get bullshit results from them, and I don't often see people even realizing this.)

EDIT: the poll authors do claim that their results are representative of the nation in some countries:

"16 of the 27 countries surveyed generate nationally representative samples in their countries (Argentina, Australia, Belgium, Canada, France, Germany, Great Britain, Hungary, Italy, Japan, Poland, Serbia, South Korea, Spain, Sweden, and United States). Brazil, Chile, China, India, Malaysia, Mexico, Peru, Russia, Saudi Arabia, South Africa and Turkey produce a national sample that is considered to represent a more affluent, connected population. These are still a vital social group to understand in these countries, representing an important and emerging middle class."

https://www.ipsos.com/ipsos-mori/en-uk/bbc-global-survey-wor...