If it's configured to do NAT instead of routing, then it's not being a router. Routing is a job and "router" describes a role, not a static property of a box. Like firewall, bridge, etc.
Routing is defined as shuffling packets where they need to go unmolested - without messing with the address or port fields. It's specced in the IP RFC's. If you're mangling the traffic, you're violating router requirements.