> He's probably ignoring the externalities like the gas leaks on the way to your house
Where I live (Sweden) and come from (the Netherlands) gas leaks tend to get fixed since they are both costly as well as dangerous. Let's assume that this is not a real issue unless you have some data which points out the opposite.
> the power plant being able to have a huge scrubber that reduces emissions
We're not talking about heating a house using coal - which is where those scrubbers come in - but with gas. Gas fired power plants do not need scrubbers since they do not produce fly ash or sulphurous oxides, nor do gas-fired heaters.
Total systems efficiency for a single-cycle gas-fired power plant lies between 32% to 38% for simple cycle gas turbines, most of those in the USA are closer to the first number. Combined cycle gas/steam turbines can run at up to 60% total efficiency which is about as high as it is possible to get using a thermal power generator [1]. The efficiency of gas-fired heaters lies somewhere between 70% and 95% or more, the upper range is common here in Europe. A good indicator for the efficiency is the fact that these appliances often use plastic flue pipes which is made possible by the fact that flue gas temperatures lie below 70°C. The effective COP for air/air heat pumps is highly dependent on the temperature difference between the hot and cold side, the colder it is outside the lower the efficiency. I don't know where the original poster lives so it is hard to calculate the expected efficiency. If it is anywhere where the temperature goes down below zero (Celcius) it is more than likely that the salesman was right since the effective COP ends up below 2 - and goes down to 1 or lower around -15°C to -30°C (depending on the model heat pump used, the amount of moisture in the air (moist air condenses and freezes on the evaporator which requires a thaw cycle which markedly lowers the efficiency).
[1] https://www.brighthubengineering.com/power-plants/72369-comp...