Sure they can. The first $107,600 of earnings, can be excluded from Federal Income Taxes. If you live in a foreign country. Look up the foreign earned income exclusion.
(Despite saying "not exactly" in the title, it is in fact exactly that. Read the details. PR residents don't pay federal income tax. There's just some caveats if you're trying to move there as a tax dodge.)
>> If you're a bona fide resident of Puerto Rico during the entire tax year, you generally aren't required to file a U.S. federal income tax return if your only income is from sources within Puerto Rico.
Assuming you're not working a multi national corp that has branches in the US (and therefore reports to the irs), I can't imagine hiding income abroad is all that difficult with a few shell LLC's and trusts.