Hi Olly,
Can you perhaps quote a bigger part of the text from the book that contains the statement? The context of that statement is unclear, and it is difficult to answer it given the available information.
Either way, here is something to consider: If you request your current ISP for a block of IP addresses, you will get a range of IPs allocated from the IP space of the ISP (we call this Provider Dependent, or PD, address space). When you move to another provider, this address range logically has to change. Now, what I find confusing about the NAT in the overall context is this: You could technically keep your old public IP addresses inside your network as you used them, and NAT them to the new public IP addresses of your new provider. However, that would create an obscure problem: Since you have moved to another ISP, the old ISP will reuse your original public IP addresses for someone else. But since you are still using them inside your own network, you would not be able to communicate with the new owner of those original IP addresses because based on your routing, those IP addresses are already reachable in your site, and so the packets would never be sent out.
As I mentioned - the context of the statement is unclear and NAT does not really fit into the picture. Knowing more would help.
Best regards,
Peter
