I don't see the comparison. The USA is a transplanted European culture that took root in North America. Those tourists really do have Irish or Scottish ancestry. Americans didn't just pop into existence, out of nowhere, in North America. Three hundred years ago, or often less, their ancestors really were in those lands and their descendants really do have (distant) relatives there.

That's quite different from baselessly claiming that your ancestors were the real inhabitants, and the current ones are just pretenders.