I think yes he did. Here's why: Jake killed Curtis in a basketball game. I think this is what got Fresh to want to escape from the ghetto. Fresh sold drugs to Esteban, a rival of Corky, and got caught, so he lied, but I think it was also to get Jake killed.
The entire movie is referenced like a chess game and from the beginning Fresh was treating everyone like a chess piece to make sure him and his sister got out of the hood. With Jake though, he killed Rosie when he killed Curtis, so his motive behind getting him removed is based on that fact.