it's simple...your Ps3 has a save of your GT academy and that's where it keeps your gold medals...not online as many of you would think..so it is hooked to your ps3 and not to your account...if you don't copy your save and put it on your office PS3 you will not see your gold medals and you will have to do it all over....
Your times are kept online and your best time will stay up as long as you don't drive faster..
i recommend to make a save of your progress on gt academy on a usb stick..