As long as the enemy player is remote, the enemy player position (and thus confirming a kill) will inevitably be delayed by the network latency (whether rendering is local or distant). That won't change.

The only thing that will change with remote rendering is that your own moves are also going to be delayed, which is certenly anoying I agree. But, on the positive side, this ensures consistancy between the view and the model, that is: you won't try to shoot at a player that is not actually where you're seeing him. That happens a lot with local rendering.