There are other possible NAT implementations that are much less like a firewall, but saying that a NAT does not provide security is a misunderstanding of the terms as they are used.
Not you specifically, but others in other threads have pointet to UPnP as proof that NATs don't provide security. If the existence of UPnP means that NATs don't provide security, then the existence of PCP means that Firewalls also don't provide security.