PS3 account sharing save data
I think it's the Console and the local profiles as the profiles have their own set of trophies and saves. Each PS3 internally would have some sort of a unique ID that is also used when registering the device so creating the exact same profile on another system with same setting and everything will not work.
Now not being able to save is a new thing for me. I downloaded a save for Agarest Generation of War when I learned that the Gods of Darkness was level 250 while I was like level 80 when I was able to fight them (I didn't really want to grind since I just needed it's NG+ Data for Zero and my next game was Agrest 2). There's no trophies with the original release but I was able to save just fine since I wanted to fight with Leo, Ellis, Dyshana and Beatrice and the party that had been set up had none of them so I saved a separate game. If you actually can't save from loading another person's save of Last of Us it could be something about the game itself.
As for trying to get around it I doubt there's a legit way which doesn't involve hacking either the system or the save. I think it's an anti-cheating system to prevent people getting Platinum's by loading someone else's save.