Yes, I think it bases it on port 5223 and the IP attached. If the PS3 can't see 5223, you can't connect to PSN and get a error. If it can see 5223 and see a Type A IP(IE 68.x.x.x) for the corresponding local IP, the NAT is Type1. If it sees type C (IE 192.x.x.x) for local IP but Type A for NAT IP, its Type 2. If it sees a Type C for NAT and Local IP, then usually your Double NATed (router connected to a router) and your NAT is Type3. Where it gets tricky is certain games use their own port for match making. So you can have a Type 2 NAT for port 5223 (For PSN) but a strict NAT for a certain game. Usually if you had to port forward the port to get NAT 2, UPnP is not working and you have to forward the port that the game uses. Some games though have a bug where the games UPnP program (thing that runs when your trying to find a match) doesn't work, and the port for match making is a random port created at the start of the session. IE, you cant get anything other then moderate for the port. There are some work around, and other complexity, but that's the general background.
Sorry if it was a little dry, meant it as a FYI for us troubleshooters, not the OP.