Nope! The bottom line is that it is possible to make a heat pump perform well in relatively cold weather through a few mechanical "tricks". There is more to it than simply speeding up the compressor, but that's the majority of it.
But we must remember, a COP of 2.0 only means it is 2x more effective than electric resistance heat. The COP will drop to below 2, as we trend beyond the below zero point.
Sooooo, burning natural gas, at 97% efficiency is still considerably more efficient from a fuel use standpoint than a COP of 2.0. As the grid is 33% efficient.
Put another way, at a COP of 2.0, the power plant is using more energy than simply burning gas in your home.
Yes, I know it may not matter to the homeowner's bottom line as energy costs vary, but it is good to understand that the efficiency is not over unity in cold climates.