A country like the US can invade any country they want. International law is irrelevant. But they can pressure a country like Switzerland without needing to resort to military action, which would be crazy anyway in the case of Switzerland.
Delaware, Nevada, New Mexico, et al. make it easy to set up shell companies. Multiple layers of corporate veils make it easier to evade taxation, if the business is so inclined. But it's also easier to legally avoid taxation, which is the goal of the next-generation tax haven.
The deal is that you pay some taxes to Delaware, as the unavoidable ones, and then use its business-friendly jurisdiction to set up a network of sub-companies that can more easily slide through all the loopholes in all the rest of the world's tax laws. So the Delaware company owns the Irish company, and the Dutch company, and the Bermuda company, and the Singapore company, and the Cyprus company, and it can optimize the on-paper accounting so the money generates the least tax possible whenever it moves in the direction of the owners. If someone goes after a mook company, it can be cut loose and replaced, but if someone goes after the mastermind company, they have to do it in Delaware's courts.
The tax haven version 1.0 relied on banking secrecy to hide financial information from taxation authorities, so they wouldn't know what to tax. Tax haven version 2.0 is about playing those taxation authorities against each other, so that all their weaknesses (relative to the other authorities) are attacked at once, and laws are only broken or ignored outside of the jurisdictions in which they are enforceable. The information is not kept secret, but it is managed so that the only entity that can see the whole picture has no particular reason to pry too deeply or to leak it to anyone else.
The Paradise Papers may spur additional legislative action, pending the results of the 2020 elections.
Those countries are huge.