I don't know why you got that idea from. Those who renounce their US citizen might have some bureaucratic hassles when they wish to revisit the US, depending on what other passport they hold, but ex-US citizens regularly travel back to the US for leisure or to see family.
wait. if you renounce your citizenship you are denied entry? wouldn't he be able to just travel to the US under the same rules as any other Cypriot citizen?
None of what the parent said is correct. You would be treated like any other citizen of Cyprus if you revoked your US citizenship. Besides that, Schmidt is part of the Davos zillionaire elite, the US isn't going to deny him access.