Whether or not that's true for your particular situation is going to be very location dependent, but I think the salesperson is fairly wrong in the general case

Whether or not that's true for your particular situation is going to be very location dependent, but I think the salesperson is fairly wrong in the general case in the US. Fossil fuel generation accounts for about 60% of US electricity and natural gas electricity generation is around 50% efficient. Another 5-10% is lost due to transmission, so say around 40% of the energy potential of a natural gas power plant makes its way to your house as electricity. Combine those and it means that every 1Wh of electrical energy generated takes the equivalent of 1.5Wh worth of natural gas. That doesn't sound particularly good, since new natural gas furnaces can be around 90% efficient, meaning that same 1.5Wh of natural gas could produce 1.35Wh worth of heating. Except heat pumps have an efficiency of around 2.5-3, meaning for every 1Wh of electrical energy they consume, they produce 2.5-3Wh worth of heat. That means producing 3Wh worth of heat with a heat pump consumes 1.5Wh worth of natural gas in the standard US electrical energy mix. Getting that same 3Wh worth of heat directly from a natural gas furnace would take over twice the amount of natural gas. Even if your electricity generation is 100% natural gas, the heat pump would be very competitive with natural gas. Now if you live in an area that gets really cold (meaning heat pump efficiency on average is lower) and all your electricity is generated by an old coal power plant (which is less efficient and dirtier), natural gas heating may actually be a greener option for now. But on average that's not the case and many places in the US have much better green fundamentals for heat pumps thanks to mild temperatures and/or lots of non-fossil fuel energy generation.