To expound a little: the same scenario applies to pure salary. If Amazon really wants to avoid taxes it can increase salary until its profits are 0.
As you're pointing out: this makes the ledger '0' in one spot, but increases it at the same rate at another spot. It's not a tax dodge, it's tax rearrangement.
Amazon either retains the earning (doesn’t grant options) and pays income tax on the retained earnings OR grants the options and the grantee pays the income tax on that amount.
What both ways are you talking about?
The 1B dollars got taxed. There was no free lunch.