Yeah, billionaires literally can do this. This isn't an American being ignorant of immigration process, this is a non-American being ignorant about what billionaires are allowed to do, that no one else is.
He was born in Germany, and holds dual US/NZ citizenship. You're right that he's rich enough to live anywhere in the world. He lives by completely different rules than basically everyone else.
You can buy visas to some countries. Then use those to access others. I think some start at $350k for one type with lots of hoops to jump through and $500k to skip the queue.