That's because it does not have an Online mode, only Local play (LAN stands for Local Area Network).
I think he's mentioning a special beta for Gran Turismo 4 that DOES include an online mode. It was launched in Japan after the game was released so that Polyphony Digital could test out the features before Gran Turismo HD Concept came around, which eventually led to Gran Turismo 5.
Nowhere is it stated he is talking about a special beta, he just says Gran Turismo 4.
He didn't mention that either. It may be the Online Test Version or not. If it's not, then why bother patching. I'm sure he knows that.