Apple pays VAT, employment tax in Ireland and certainly a couple more. They avoid paying
corporate tax by using a Irish sandwich Double Dutch tax structure (where you create subsidiaries of subsidiaries, and pretend all the value creation happened in over-seas territories where corporate tax is negligible).
Apple is probably right in saying that the total of VAT, employee tax, etc. is the largest in Ireland, the US and World: they are the largest company in the world, so that statement should be fairly obvious. If someone who makes 1M$ per year pays 0.5% taxes, he still pays more than someone who pay 20% of their 24k$. That’s why this statement is seen as disingenuous: the ratio to your revenue is was matters.
The European Commission, the vast majority of observers and almost all Hacker News members are right in saying that they paid virtually no (0.005%) corporate tax, because that was the point of the statements they made to tax authorities around the world.
On whether what Apple did was legal: the stated that their all their value creation happened in the Dutch Antilles, which is patently false. That is nothing short of lying on your tax form. The Irish government accepted it because they were strong-armed into accepting that or seeing jobs go elsewhere. That type of coercion is also something that this letter lies about.
In the US, John Oliver pretending he is the Head of a Church whose main tenet is his personal enrichment is widely accepted as a legal, and deserving of a tax break; in the EU, such statements are considered disingenuous (that’s the fancy word for “bullshit”) and treated accordingly.