Quote Originally Posted by Pinnacle
It seems like a router could be configured to recognize any particular range of IP addresses to be private so that it would properly translate them if someone wanted to leave the private network.
In theory that would seem to be so. I can't speak authoritatively for the internal design of routers, but what would prevent the system you've mentioned, would be that it isn't possible to exclude wanting to connect to the same IP address on the internet as you've chosen to use on the private network. This would produce a situation where the router, which routes by IP address, can't tell which of the two same addresses a packet needs to go to. ie in this case NAT would fail.

The chances of this actually happening are tiny, but it mustn't be capable of occurring. So using mutually exclusive IP address ranges automatically prevents the possibility.