I think the misunderstanding is of how these devices measure power. The SWR is calculated by measuring the forward and reflected currents and calculating their ratio, it does not have any specific units, one is relative to the other. For power they only measure the voltage at the input or output socket, either one but not both. The power is calculated using standard Ohms law (V^2/R) but assuming that the antenna load impedance is purely resistive and 50 Ohms. That means that the power measurement is only accurate into a 1:1 SWR, if it deviates, the power measurement is less accurate. You really need a pure resistive dummy load to measure power accurately.
You can test this easily by disconnecting the load completely and running low power to it. The power will appear to be unreasonably high considering nothing is actually being fed to the load at all.
Brian.