Politicians in developed countries don't have enough money to pay off blackmailers. That's why - except in dictatorships - sleazes tend to avoid politics. Self-made billionaires like Bloomberg and Jobs are far too busy building their empires to dabble in sleazy affairs with married women, which take up considerable amounts of energy and time. Women have be courted and cajoled into jumping into bed, which is why many charismatic, popular and good-looking showbiz figures and sports figures prefer the company of prostitutes. And for politicians, the risk of exposure isn't limited to chatty paramours - it extends to service personnel at restaurants, bars, hotels, et al, and well as the relatives and friends of the paramour, all of whom could spill the beans for mere thousands of dollars to a newspaper or news network.
An island means the 'help' won't just be running off to tell what they may have seen, and communications could be monitored or simply controlled.
Knowing what sort of 'vacationland' that was would be reason enough for people who did not desire to avail themselves of the offered 'services' to just avoid the place, lest they be lumped in with the regulars.