The EU does not tax companies. Individual countries tax companies. What the Eu does is to ensure a fair playing field and make sure that individual countries treat all companies in the same way and that one country does not set up sweetheart deal at the expense of others. Apple is not the only company to have suffered this fate and they will not be the last and while many of these companies are American not all of the are.
to be fair, that is not entirely accurate, while my example is peculiar due the economic situation in Greece, but even before this ****storm that has befallen this land, companies in Greece paid more taxation (or at least they were obliged to) + a 55% advance payment of next year's taxation based on the previous fiscal year's tax calculation. I am quite sure this doesn''t happen elsewhere in the EU. And now, they wan't to raise this advance payment to 95%. So EU having a fair playing field doesn't sound realistic.