LION/LIPO battery capacity measurement
You don't need to do the debunking, it is already done, see the Lygte website



As one can see, the measured capacity even at lightest load of 200 mA yields just about 1200 mAh instead of advertised 6000 mAh.

And yes, running a protected (in a standard way) cell down will result in 0 terminal voltage, somewhere at below 2.5V. The cell will disconnect under load. However, after a few seconds, the voltage will re-appear, due to small no-load recovery. In any case the cell will happily assume charge if plugged into a charger, and no harm  will be done to it. This is what the protection is for. More, there is not much energy left in the cell when its voltage is below 3V, a percent maybe or less, so the difference between discharging to 3 V and down to protection limit can be safely ignored in capacity measurements.