I think its by design. I can't imagine any other reason for Amazon to show me "Will arrive tomorrow via prime shipping" on the item page and then, only when it is in the cart showing me actual delivery being 4+ days.
I am guessing that since it is such a hassle to go back to the cart, pull the item with the false shipping dates, and then find another similar item with good shipping dates, add to cart, go through checkout, find out that shipping is actually 4+ days, rinse and repeat until you either get lucky or give up, they're probably not going to fix it because it makes them more money to keep you frustrated.
I am guessing that since it is such a hassle to go back to the cart, pull the item with the false shipping dates, and then find another similar item with good shipping dates, add to cart, go through checkout, find out that shipping is actually 4+ days, rinse and repeat until you either get lucky or give up, they're probably not going to fix it because it makes them more money to keep you frustrated.