You can only run the game on PS3 under the PSN account it was purchased / registered under. This has nothing (directly) to do with actual linking of the PSN account to SE service account - it's simply a restrictoin imposed by Sony / SE to allow to use the game only by the purchasing account. This happens already BEFORE / independently of linking PSN account to SE service account.

Short answer - each player (even on the same PS3) with own PSN account need to purchase own "copy" of the game.