Your inverse isn't correct. The correct inverse would be to look at the countries that do have tax.
Let's look at Guinea
There's the tax information:
http://www.doingbusiness.org/data/exploreeconomies/guinea/pa...
Oh by the way it's the poorest country in the world 2017.
I did take a look at what jacquesm suggested and here is a list of countries that have no income tax.
* United Arab Emirates
* Oman
* Bahrain
* Qatar
* Saudi Arabia
* Kuwait
* Bermuda
* Cayman Islands
* The Bahamas
* Brunei
Now you could argue that the countries are rich countries and the only ones doing well are the native citizens or that two of them are tax havens for the rich. But hey that's not what he said.
And the moral of the story? Unquantified generic statements are usually bad. Don't do it. No matter who you are, don't do it.
He also said "no taxes", not "no income taxes".
Especially because those people often are talking about countries with some form of democratic socialism (where there are a number of strong success cases), and instead frequently put forward libertarianism - which is a completely untested government form in any country.
That is one of the reaons I moved here. Here more about this: "8 reasons why I moved to Switzerland to work in tech" https://medium.com/@iwaninzurich/eight-reasons-why-i-moved-t...
No one is thinking there should be no taxation, just that there's a sizable chance here that the government is in the wrong. To reverse your argument: please point me to this magical utopia where the government is always right and they never abuse their powers.