Ground source heat pumps are not air source heat pumps. They’re not an option for people without either very large gardens for horizontal installation, or access for very large machinery to dig the holes to install them vertically.

The claims you have seen likely came from a pro-carbon lobbyist or someone with a badly-installed heat pump. Air source isn’t as efficient as ground source but they are cheaper to run, as long as the house is reasonably well-insulated, has large enough radiators or underfloor heating, and enough air circulates around the pump.