On January 4th, I ordered two items from Amazon via Purse (affiliate link -- if you join Purse through it, once you've spent $100 both you and I receive $5 worth of BTC).
Both items are "Prime" eligible and claim two-day shipping if ordered directly, and on the Purse site there's a little picture of a truck with the words "Fast Shipping" next to it accompanying each item.
Purse got the Amazon order in pretty quickly, so I've got no heartburn with them.
But today is January 7th, and Amazon's "track package" page for them says the items still haven't even shipped yet and that I shouldn't expect them until the 14th.
That's not "fast shipping."