You make an example out of them with your vastly superior firepower. Galt's Gulch wasn't just a bunch of rich dudes hiding out, but also the greatest technology center in the world along with a very competent military force. Thus is the power of science fiction.
Is Thiel planning to have a navy as well?
Sounds like he'll lean on some developed world navies. But if he's planning to go it alone, yes. They could always just not put these things right off the coast of Somalia or North Korea. Pirates aren't found everywhere. Don't put them next to poor people or authoritarian states. That leaves a lot of ocean.