I've had 250 orders with Amazon last year alone, all of them with Amazon Prime - I've had things which arrived a day late, but literally everything dispatched the same day, always. I'm in UK.
Amazon 'told' you they dispatched the same day... but they would, wouldn't they?
Well I always had a tracking number...and parcels which were late were always shown on DPD website as being stuck somewhere in the country, not in Amazon's warehouse.
Aha, I'm used to Amazon Logistics delivering all Prime parcels!
There isn't a lot of guessing when you have a tracking number.