You need a clean background to move to another country if you're not a European. I specifically had to submit a Canadian RCMP fingerprint based background check when I moved to Iceland. EU nationals have it much easier, since the relocation process in the EU does not require that level of scrutiny.
After I replied to you I asked a European national who I know if they had to submit anything. They did not, and only found out that it's part of the process by talking to American expats. So apparently this is not common knowledge in the EU!
I assume they're suggesting create a false identity, and pose as a foreign national illegally living in the United States.
It's a rather ...unconventional suggestion, that clearly was not thought out. There is a high risk someone doing that ends up stateless, i.e., with no documentation or paperwork establishing citizenship in any country. The US may arrest such a person at the border - and then imprison them - and then try to deport them back to their country of origin. But what is your country of origin? It may mean a stay in immigration detention indefinitely. There's no guarantee authorities would believe a claim of US citizenship at that point. Citizens who've gotten in that position (usually cases of mistaken identity and/or misbehaviour by US customs) have been deported, and they don't always make it home. It is a potentially Kafkaesque nightmare and I would not advise intentionally putting yourself in that situation.
U.S. Customs and Border Protection will happily reply to emails explaining exactly what I said is what in fact happens. You don't have to travel to Arizona or Texas to see it first-hand.
Rather than constructing an imaginary straw man detached from reality, please try to reply to the comment and the facts with external links to refute the information. I'm more than happy to provide further counter-factual information to whatever hifalutin nonsense is offered, as if this isn't a statement of fact.
What I'm describing is what actually happens today for the overwhelming majority of border crossings. :)
