> Sure, but the Internet will not route packets going to RFC1918 addresses
This is about RFC1918, not NAT.
> So, if you're using an RFC1918 address on the LAN side of the router like every sane admin, packets that actually arrive to the router from the Internet with an IP address other than the router's own IP address will get dropped.
This is about reverse path filtering, not NAT.
> And those that arrive at the router with the router's own IP address and a port that doesn't correspond to either an open connection or an explicit port forwarding rule will also get refused.
And this is... actually not true. If there's a server listening on the relevant port, the connection is accepted.