If the item you're ordering is out of stock or unavailable to ship immediately, the shipping method time starts when the item ships. For example, it will take two business days after an item ships to reach you with Two-Day Shipping.
Amazon could easily make the case that even though the item you ordered was "in stock," it was still unavailable to ship immediately due to warehouse backlog or other operational reasons.
Even so, they regularly fail on even delivering two days after shipping, and even more often on one-day.