What Misslehead said was partly true. When you have internet connectivity (PS3 will check this by signing on to PSN briefly and signing off without notifying you) you will get three PSN sign in screens when you load up GT5. The secret menu only disables one of three leaving two more. The first sign in appears with the Gran Turismo 5 logo which is the one that can only by the secret menu, however subsequent sign in messages appears when you get into Gran Turismo's main screen as well as going into GT mode for instance. Those cannot be disabled, it seems they are probably hardcoded into the game.
There aren't much other choices to avert these, apart from either physically unplugging network cable (if using wired connection) or disassociating with the AP/router (if using wireless connection). One could probably also somehow turn off network connectivity through the XMB though I've switched my PS3 to a foreign language in which I'm still trying to learn the various wordings and hence unsure if there's such an option or not. Unless if one has a good grasp on making the most of their network connections between their PS3 and its connection to the internet (i.e. able to utilise their modem/router/AP/etc to its maximum potential) there isn't much other choice apart from the two basic methods mentioned in the first sentence of this paragraph.