Ah, I was using the term incorrectly. I meant that one must renounce their citizenship in their birth country to be completely free of taxation. Expatriation can be hard. Renouncing birth citizenship extremely difficult if not impossible in some situations (catch-22s, etc)
For US citizens, to renounce you need to prove that you've paid all income taxes over the previous 5 years, pay an excise taxes on all assets being taken out of the country (which I think is %1-2%) and -- here's the kicker-- get permission of the federal government to be allowed to renounce your citizenship. If they think your earning power is significant enough, they can deny you by claiming your "renouncing to avoid taxes".
However, if you live outside the USA full time, I believe that the personal exemption on income is around $80,000. So even if you're making millions, if you pay yourself $80k or less, you can avoid income taxes in the US on your worldwide income.
Thus, holding stock in a startup that is appreciating avoids taxation, however, if you ever sell that stock, then you'd be realizing the gain and run into the issue.
PS - of course you're right that some countries simply won't allow you to renounce, and that might even end up being the case for some US citizens. I'm just giving the information I've been able to gather on this topic, not really disagreeing with you.