Online multiplayer game: How to elegantly deal with this rocket mechanic?

Question

So I'm making an online multiplayer game where you can shoot rockets. The person shooting the rocket is in first person view. The person being shot at is in 3rd person view with the camera looking down on the playing field.

Currently the player being shot at decides if they were hit and die. I could make it the other way around and the shooter decides, but I will have a problem regardless as detailed below.

The issue comes in where the player who is shooting the rocket sometimes thinks their rocket hit the opponent, however due to pings not being zero they dont realise that their opponent dodged the rocket from their perspective.

Obviously if the opponent was in first person it would be harder for them to tell if they were hit or not, so you could just have them die and they'd be none the wiser (basically its hard to know exactly how wide your hitbox is when you are in first person so they'd probably accept that they got hit, and since the person shooting the rocket thinks it was a hit everyone is happy). However since the person being shot at is in 3rd person view its pretty obvious to them if the rocket looks like it hit or not. You have that 3rd person perspective where its easy to tell.

Should I just dump this rocket mechanic entirely? Or is there an elegant way to deal with this so both players are (at least reasonably) satisfied with the result (i.e. did the rocket hit or not)?