Nope, 3GB is the initial download size required to start playing the game (PlayGo system, folks).And the game is most certainly not 3 GB - I believe it's around 17-20. That could be part of the issue?
Hmm, I've faced this problem and was able to solve it by reinstalling the game (because other things didn't work).
Sorry to see it's not always working.
Thinking of it, I wonder if I haven't read someone on GAF saying (s)he had to boot his(her) console in maintenance mode and rebuild the database to get the problem solved.