1: DELETE the Fallout: New Vegas game data from the Game Data Utility. Do NOT delete the DLC data (also found in the Game Data Utility). Also make sure you select the GAME Data Utility, don't accidentally select SAVE Data Utility.
2: After it deletes, start the game up from the XMB. (OPTIONAL: This is NOT necessary, but, before starting the game up, copy your SAVE data to an external source, like a flash drive, memory card, etc. I DID NOT do this, and NONE of my data got corrupted, but still, it's always good to be safe just in case your ps3 decides to be funny.)
3: After you start the game, you'll be asked to update to version 1.07. DO NOT download the update yet. Instead press O to cancel, and let the game continue on and install the game data.
4: After the game data installs, quit back out of the game. (OPTIONAL: At this point I reset my ps3. I don't know if doing that actually mattered or not. So you can try it if you want. Resetting may or may not make a difference.)
5: Start the game back up again. This time, when it asks you to update, do it.
6: Load up your game and play.
So that's what I did. Like I said, I may have just gotten lucky. Those of you who are having problems with the game like I was, try this out, and post your results here. Let me know if it worked or didn't work, or even if it at least helped a bit. That way if this gets proven as a fix, we can spread the word and help others out. So far it's been working for me, but we'll need more results because mine might be just an isolated case. Anyways good luck everyone, hope this helps.