This method is often used by wealthy people to not only avoid paying taxes, but to protect their money and/or assets from seizure in case of divorce, bankruptcy, and/or other reason for taking their stuff away.
I have seen many cases where a divorce was filed, but the spouse was unable to claim on offshore assets because they are not visible to the current country where the divorce was filed.
This is not new and is always a problem for tax collectors and government alike. Imagine a person who is retired and is collecting a pension. He/she can be collecting pension in one country and hiding a mansion with twenty trillion dollars in a bank somewhere else.
Furthermore, a person could declare bankruptcy in one country to avoid paying his/her debts, and move to another country where his/her trillions is waiting.
If the IRS goes to Russia to try to get an American’s bank records, the IRS personnel will probably be jailed. Russia does not like the American government very much.
I find it funny when I look at the tax form and see a couple of lines for “Write down any other assets you own in other countries”. Is it possible that the tax man can check your name in every country in the world? Possibly, but only in allied countries.
Therefore, if you have some money lying around, you can hide it in some foreign bank.
An article where the US is cracking down on asset hiding can be found at http://www.nytimes.com/2009/01/10/your-money/brokerage-and-bank-accounts/10wealth.html
Another article that talks about where the money is hidden http://businessfinancemag.com/article/gao-big-us-companies-love-tax-havens-0120