If the country you are physically in wants to (e.g.) tax you, they can. (There are, of course, many more nefarious possibilities than taxation.) This is, I think, true in an "in accordance with international law" sense (though there is the possibility that a bilateral double taxation treaty might apply) and it is certainly true in a "who's to stop them" sense. (And if we're hypothesizing that the person is physically located in a corrupt/war torn country, the latter would probably be all that matters anyway.)
Nothing stops you opening a company in Estonia now, but that does not mean you would only pay corporation taxes there (they are at 10% when distributed as dividends), your physical location plays a role too.
Can't see why a US or Estonian company (whether or not you are a director is irrelevant) can't hire you to do some work. Unless you don't have work visa in the country of your stay.
I don't think it works for money laundering in any way.
My understanding is that this status allows you to form companies, open bank accounts and sign binding documents just like someone living in Estonia. And that is pretty impressive.
Add cryptocurrencies into play, and whole new world of companies is now suddenly possible.