What does "You did not earn a trophy" on the PS3 mean?

Question

So the other day I was playing Cars 2 on the PS3 and we got the in-game badge "Tokyo Vandal" and soon after at the top of the screen where it usually would have shown "You have earned a trophy. Tokyo Vandal." it showed "You did not earn a trophy."

I was playing multiplayer and the same trophy has been gotten on some of the other "users" on the system.

Answer 1

According to different sources, and also @Wondercricket comment:

This happens when you earn a trophy on your profile with someone else's gamesave.

or

It's because they used a game save that was linked to another PSN account.

_{Sources: here, here and here.}