Where to Buy ISBNs and Where Not to Buy Them

There is only one place to buy ISBNs in the United States: Bowker (The United States ISBN Agency). In the UK, it is Nielsen (Nielsen UK ISBN Agency). Each country has exactly one agency allowed to assign ISBNs.

Why then do some publishers/printers/people claim they can sell you an ISBN? For instance, both CreateSpace (Amazon's printing company) and Smashwords claim they can sell you an ISBN. If only Bowker is permitted to sell them, why is this? (My explanation will use CreateSpace to...