How to not pay your taxes legally, apparently

Another way for Americans is to qualify for the FEIE by working a remote job in a foreign country that isn't good at collecting taxes.

Wouldn't claiming an exemption for foreign taxes that you didn't actually pay be fraud?

That is "only" ~100k or a so a year and if they aren't in the USA more than ~30 days a year. Small potatoes and arguably makes some sense.

Yes, but I’ll give a concrete example: I was an expat in New Caledonia. They have (or at least had) no income tax. The salary was below the amount that the US taxes for folks who are legitimately living outside the country, with a fair portion coming from a difficult to quantify housing subsidy.

Sure but the premise is "legally" not "can get away with it"

(Though, to be fair, I guess those two things aren't that different in practice)

You don’t have to claim to pay taxes. It’s not the same as reciprocation.