Actually, US citizens (and residents) are taxed on their global income. You also must declare all year-maximum bank account balances and/or investments globally if you have assets over $10k (aka FBAR) or risk huge fines or jail. This is why the "Swiss bank account" of yore is deemed tax evasion - there is no legal way as an individual to avoid Uncle Sam.
You can receive a credit for foreign taxes paid but its not always 100%. US There is an exemption if you actually reside overseas for a period (aka. Foreign Earned Income Credit) but the cap is small, maybe $100k or so.
Apple is dealing with a different area, that of foreign subsidiary corporate profits. Repatriating that money to the parent means the parent is recognizing the earnings of the foreign subsidiary for tax purposes.
It actually really sucked for US citizens overseas, who may have moved when they were children, or when they dodged a draft in the 60s, and never filed their 1040s or FBAR.
The worry recently (as the IRS has been cracking down as of late) is any re-entry to the US with a US passport would lead to a massive tax bill for all foreign income over the past 40 years. Or for Canadians living in Florida who never declared their Canadian retirement funds. Fortunately the IRS offered amnesty in 2008-2010 to most to "come clean and get no penalties".
Now, Apple's cash takes quite a (currently legal) trip around the world, but the basic principal is the same.