> As a private tax payer - the IRS would have no problem calling this a tax-aviodance "scheme" - and hit me with a big tax bill and penalties.
That's not actually true. If you could figure out a way to make your salary accrue overseas, you could shift it to a low-tax jurisdiction too. The IRS is actually very anal-retentive about following the letter of the law, and doesn't just capriciously decide to treat the same situation differently depending on who is on the other side of the table.
The difference is not that the law is designed to benefit big corporations, or that big corporations don't follow the law, it's that big corporations with international presences have a more complex tax situation than you do, which they can leverage to minimize their tax liability (in the face of tax haven jurisdictions).
There is pretty much no doubt that everything you earn as a salaried employee in California ought to be taxed by California and the U.S. But if you're a multi-national corporation, why should the U.S. collect taxes on all of your income when part of it may be due to, say, a product made in China being sold to someone living in the UK?