Shouldn't happen to a fully patched up to date system with a stealth mode NAT router between you and the net.
Of course there's a window of opportunity before you download the service packs and patches - which you should of course do before worrying about any AV stuff - but still nothing should get past the stealth mode NAT router (or other hardware firewall of your choice).
What a load of old nonsense.
Rule 1 of computer security : Security by obscurity is not security.
NAT was not designed for security. NAT was designed to provide a way to reduce the number of IP addresses that have to be allocated to users.
Lots of ways for things to get past NAT. One of the simplest examples is the human sitting behind the computer