

You are right. My comments shouldn’t be taken as precise advise for specific situations, but I stand by the generalities. I’m general though, if a family with less than a grade 5 education can make a cross-continent trek in hopes of a better life, most US citizens are well positioned to immigrate elsewhere.
You only have to pay them if you move back to the US (and want to work). It’s not like other governments disclose your finances to the US.