I used to order a lot of stuff (mainly books) from Amazon and unfortunately have experienced a lot of this discrepancy between the 'usual' despatch date on the item's web site and what Amazon actually told me. On one occasion I ordered a book which said on the web site that it is usually despatched in 24 hours. The time they gave me in the confirmation email was 4 - 6 weeks! I emailed them, asking them about the discrepancy. They replied stating that the time stated on the web page was approximate. There's a bit of a difference between 24 hours and 6 weeks! In the end I cancelled the order and ordered the book at a local independent bookshop and had it within 2 weeks. Now I very rarely use Amazon - it's too much hassle.
I know there are a lot of Amazon 'fans' out there but this is just my experience.