I figured it out, and I can confirm that this also worked for me.
For those not familiar with playstations (As I am):
1. Completely delete the game (if it is already installed). This is done from within the System settings: Home Screen -> Settings -> System Storage Management -> Applications -> Options / Delete, Select Need For Speed, Confirm
1-a. Go to the Store and start downloading Need For Speed
2. Shortly after you start downloading the game, a 2nd notification will pop up saying "Update File: Ready To Install." At first I thought this was the PlayStation telling me that the game was ready to install, but it is actually the patch.
3. While the game is still downloading, navigate to the notifications section of the home screen, highlight the "Ready to Install" message, press Options, and then Delete. This has the added bonus of making NFS immediately playable, as I beleive the patch forced the download to complete before being able to play the game.
4. At this point you should be able to Play, and you'll see the warning others had mentioned. Go ahead and play the game.
5. Play through the game and complete the tutorials for both Cop and Racer.
6. Once you've completed both tutorials, it will dump you back to the "Installing Game." screen while the rest of the game is installing. If it is already installed, I would assume you could continue playing. At this point the previous instructions would apply, just exit the game and install the patch and you should be good to go.
