Do you wait for the kettle to turn itself off before using the boiled water?

To settle this you need to apply proper science. Some equipment will be needed. You need to aquire a way of measuring atmosphering preassure (or altitute as it affects the boiling temperature) ,measuring temperaure (calibrated) , purity of water (you will need a laboratory for it), asses the scale buildup in your kettle (this will affect your boiling temperature over the lifetime of the kettle) and probably few samples of kettles to analysie the thermal strip quality (this part is responsible for switching kettle off). You should aquire a decent stop watch as you might find there is a varying delay between when water boils and switch-action (this can vary from model to model). Also you would need to agree on definition of "properly boiled". I love your little dilema as you are both probably stuck! From the TEA point of view there might be no difference between few degrees of water temperature, biggest impact will be the brewing time (or fucntion of time and temperature). Seriously it is all mental games, you can try few blind tests you should not be able to tell the brewerages apart, maybe with sufficient time you can brew tea from cold water and later reheat it for the test - FUN. Good luck with your experiments.