How could there be a sync issue on a split screen multiplayer game?
Both players game data is being produced by the same console.

I think the bomb issue is an online problem ,same as the dreaded non functioning weapons pads which ruined a few races again last night,as well as the ability to fly straight through an opponent [collision detection not in sync]

I doubt if these issues would be replicated in split screen mode.
Though stranger things have happened,but I'd be surprised if it did.