There is an arrangement for citizens of the three Pacific Island sovereign states of the Federated States of Micronesia (FSM), the Republic of the Marshall Islands (RMI), and the Republic of Palau, to travel visa-free and live and work in the US indefinitely.
This applies to citizens who are:
"...citizens from birth or independence, and to naturalized citizens who have resided in the Federated States of Micronesia (FSM), the Republic of the Marshall Islands or Palau for at least five years, excluding those who acquired citizenship by investment." (Source)
My question is that if someone becomes a citizen by means of investment, how do the Immigration officers know about that at the time of entry to the US, since they can travel visa-free? I don't think passports mention who became a citizen by what method.