Guardian explains why Apple does't pay taxes in Ireland

Money quote:

Their boards have been able to tell the Irish tax authorities that Kearney, the sole Irish-resident director, cannot be judged to manage or control these companies, and that important decision-making rests in California.

As a result, AOI and others are not deemed tax resident in Ireland.

Meanwhile, because these same companies are incorporated at addresses in Ireland, under US law they appeared not to be tax resident in the US either. "Magically," observed Senate committee chair Carl Levin, "it's neither here nor there."