This article is mere attempt at convincing wealthy investors to buy some property through Sibarth Real Estate.
It certainly does not paint a true picture of what the actual living on the island is about.
Regarding the "no income tax" status, as described a new resident must be on the island for at least 5 years before getting it (including French citizens). Meanwhile income taxes must be paid at the applicable rates found in mainland France (as any other resident making a living on French territory):
Income Tax Rate - 2016:
30% of yearly income if between 26,000 and 72,000 Euros
41% of yearly income if between 72,000 and 152,000 Euros
45% of yearly income if above 152,000 Euros
Most (new) residents will see their income taxed at 41% to 45% for the first 5 years on the island. And that is if you have the right to work!
A foreigner (non EU) moving to St Barths does not have the right to work on a normal visa. Buying property might get you the right to reside temporarily, but certainly not the right to work. It might be ok for retirement (with foreign income - not taxed). However this is not so great for a family which needs to see some regular income while on the island.
Living here certainly offers a quality lifestyle but it is not for everybody. The island is small and although it's great on vacation, it does come without some difficulties when living all year round. I wish the article would be more honest in that matter. Access to health care is a major issue, so is education, just to mention a few....