>> What services are Apple not paying for already?
Overseas, Apple go to extreme lengths to conceal the profits made in that country (see "transfer pricing"). This means they pay astonishingly little tax in said foreign countries, eg Australia.
It seems fair to me that where profits are made in a country, which depend on the infrastructure of that country, those profits should pay tax there.
Imagine you live/work in - say - Belgium, and earn money there. You live there, you enjoy the benefits of Belgium's infrastructure. Does it seem fair to pay taxes in a country with low taxes and less infrastructure such as, say, Liberia? To me it sounds like tax dodging.
Why is a company any different?
It's true that Apple pay a lot of tax in USA. But compared to their profits it is probably quite low compared with the taxes you presumably pay on income. (I'm assuming you are American as you don't seem too interested in taxes anywhere else).
USA has an odd (possibly unique) scheme whereby any repatriated overseas profits are still due to pay US tax, less any overseas taxes paid. But as they pay very low overseas taxes, despite earning their profits in similar taxing countries, so they are unable to repatriate said profits. Hmm, could that possibly mean they have manipulated their accounts to do that? Surely not ...
So, basically, Tim Cook is taking complete rubbish.
Apple - pay your taxes!
Ditto all other corporations, eg Google, and probably every other big multinational.