If they set up a medical tourism business just offshore, will that be unremarkable or destroyed?

It is unremarkable in that medical tourism is available in many countries already. Making it much cheaper might have a dramatic effect. or not.

Yes, there are certain bounds that the US imposes, but are there so many?

ETA: I see that MM gives medicine as his particular example of what won't succeed. And Patri answers that medical tourism already exists. I don't think that's a great answer and the rest of his comment is a weird mix of practical (cruise ships do violate labor law) and naive (written law). But I don't find MM's short argument convincing, either.