You don't use your own word when you summarise someone argument. If that is the case, this become your own argument rather than someone argument. So you cannot said someone said this and instead you have to say I said this because the meaning has been changed.
The second thing you have cut off the reason of the argument and makes the meaning sound awkward. If you want to say what someone said you have to check with that person whether you have interpret correctly or "Had I missed something"
