You misunderstand. These are not tax cheats. The law has turned the seven million Americans who live abroad into pariahs. Very few foreign banks will open accounts for them, as they don't wish to incur the cost of complying with the US's new, draconian reporting requirements.
I can't even begin to tell you how many US citizens I know living abroad who have been off the IRS's radar for so long that they could give two shits about any of the tax requirements they have. They haven't reported in years and don't plan to.
Iirc, if they have deposits over $30k they will have to sign a form declaring that they are (or are not?) a US citizen, that's what the US law requires of foreign banks.
This all changes with FATCA (Foreign Account Tax Compliance Act). Shortly they will not be able to open new bank accounts overseas and will have their current bank accounts closed if they are American citizens - and have not filed their U.S. taxes. Nearly all banks internationally are onboard with FATCA which was pushed as an anti-terrorism initiative to Know Your Customer.
There are still a good deal of foreign banks that don't do business in the US and don't give a rats ass what US law says. Additionally, many rich americans living abroad can easily get a second passport in various countries through "investment" locally. Then they use those passports to open bank accounts. For cryin' out loud, this is a joke to sidestep if you have money.
You might want to check that "nearly all banks internationally" statement, as it's bogus. I know this for a fact.
Probably more trouble using them than they're worth. Sadly, the major banks are going to comply with US law.
See my edit. For example, the number 1 Russian bank Sberbank, will not comply with new US/IRS reporting laws. It just won't. Nor will any of those in the top ten. No trouble at all to use those.
Easy to say. I'm not moving cash to a Russian bank. I am wondering what happens if I simply check 'No' on the form, though.