It isn't possible for anything to get thrown off if you have no deaths and don't make any mistakes; the only way for you to have had the fire debuff is if you messed up and got hit by the out-fire when the tether wasn't on you. Ice is a set rotation and will only change if the next person on the list is dead.

You cannot debate this point. You're adding an extra step when it isn't needed and increasing the chance of failure by having your default be a habit that can potentially kill you if you don't notice your debuffs. By defaulting to staying out if you got the odd fire, you will never die to fire (unless other things went wrong and too many people died, in which case it is very difficult to recover anyway since a fire out may have to be a fire in, etc.).