PS3 Error 80010514

[Melfice]

I've already posted this on the official Playstation forums, but I figure it might help posting here as well.

I've recently bought GT5, but after installation I got error code 80010514.
I've read somewhere that this problem, despite Sony's insistence it's a hardware failure, is caused by a faulty disc.

Cue me trading it in for Assassin's Creed Brotherhood, and lo and behold, again the same error code.

In both situations, I've tested my other games and a couple of Blu-ray movies, and they all work so I'm sure it's not my blu-ray reader that's faulty; and what would be the odds of me getting two faulty discs in a row for two different games?

I have an old model PS3. Possibly a Fat 40 gig. In any case, it was bought just after Backwards compatibility was removed.
Any suspicious man would think Sony's trying to hawk a new PS3 to me by rigging their new games to not play on the old PS3's, but that has to be nothing but bullshit conspiracy theories.

So... hoping anybody here has had the same problem, or knows what to do about it. (Nikose, possibly?)