Do trophies count as characters being in the game? Like Brawl?

I've recently removed a few different characters with Brawl being one of the games they've been in, and it just hit me, I think it was there because they were a trophy in the games.  Trophies are just collectables you find in the game, and are made to represent tons of different characters from Nintendo's history.  Would these be considered as being a game a certain character was in?

Take Louie for example.  He was in Pikmin 2, but he has his own trophy in Brawl, I had already removed Brawl from the list because I didn't realize he was added in Brawl as a trophy.  So does it still count?

I don't think trophies count its the same thing as a character being mentioned in a game but never appearing really.