Doesn't matter in the long run, corps and individuals who want to tuck money away will find a way to do it. All this is going to do is add an extra layer or layers to hide behind, but the wheels of gov't turn slowly, and big corps and individuals have tax attorneys who find the loopholes and the leaks, and they'll move quicker than the gov't can ever hope to create laws. They may catch a few smaller corps and individuals who will find no advantage to adding the extra layer(s) of anonymity, but the big corps and the mega-rich will pay the extra because the savings is still too significant.
For example, this is from the article:
For individuals, Obama will propose shifting the burden of proof when the IRS believes money is being hidden offshore. In cases where individuals bank with financial institutions that haven’t agreed to report certain account information to the IRS, the individual will have to prove he or she doesn’t own the account, rather than requiring the IRS to prove ownership.
How do they not already know an individual owns the account, you might ask. What individuals do is go overseas, open up a corp, loan the money to the corp, make yourself the officer, and the account isn't a personal account, now it's a foreign corp that makes money but it's not subject to US taxes.
Now you have to prove you don't own the account. Easy enough. For a fee, some gov't will be more than happy to create a person who never existed who then becomes owner of the account. So who owns the account? Ping Pong Tang owns the account, just ask China they have the paperwork on him. In the meanwhile, John Smith still controls the account (wink, wink).
That's probably too simple, there's more complicated ways to create a maze for any gov't snoopers, no doubt. Like I said, they'll add layers.
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