Downloadable content and trophies question

[JOKA_]

There are games that have DLC that add trophies, LBP is as example

I think it works like this:

You only need to get the the trophies that originally came with the game in order to get the platinum trophy. However if you get some DLC with added trophies, you will no longer have 100% of the trophies but you will still have the platinum.

If you have the platinum trophy in LBP and don't have the DLC, and then you compare your trophies to someone who has the DLC, it will say that you have the Platinum but you only have 80% of the trophies.