The myth exists because the US is probably 10-20 years behind Europe and China in terms of HVAC and insulation technology. I recently had some reasonably high efficiency heat pumps installed at my house, and I’ve been very unhappy with the low temperature performance. It doesn’t even get very cold here—rarely below 5F (-15C) and a record low of -8F (-22C). The heat pumps I got (recommended by the well-regarded local HVAC company) operate at just 40% of rated capacity at 0F.[1] Meanwhile, Chinese and Japanese-made inverter driven heat pumps will happily go down to -5F at 100% of rated capacity, and -22F (-30C) at 80% of rated capacity.
[1] You can of course get a much larger heat pump to compensate, but that leaves the unit way over-sized for cooling loads.
I recently saw a transport nerd claim that US and Canadian (though interestingly not Mexican) busses were substantially and objectively worse in build and ride quality than European busses, even when they share the same engine components.
Which I guess similarly explains a lot of weird conversations and people talking past each other where busses are concerned.
In my local market, if you ask an installer for a heat pump, you get something from Japan or Korea. I’ve never encountered an American unit.
(I’m referring to normal air-to-refrigerant-to-air heat pumps. I know of a really weird system that is thoroughly American and an utter pain in the arse to replace because it’s specialized and undocumented. It’s quite loud, too, because it’s single-speed, and that single speed is waaaaay too high.)
The Asian brands make products for the US market—often through subsidiaries that were originally US companies, such as Goodman and Amana. Basically stuff that complies with US codes and standards, and that US HVAC installers can fix without learning anything new. Daikin makes a ton of stuff they don’t sell in the US. Owens Corning makes high density fiberglass batts you can buy in Canada but not in the US.
Sounds like the units you are describing don't have an efficient (read 'big enough') heat-exchanger which is why they aren't being effective in not-so-low temperatures. The temperature of the cold-side should not be below outside ambient temperatures if the heat exchanger coils are sufficient.
In other words heat-energy should be going into cold side of the heat-pump (even at a low temperatures) at the same rate as it is coming out the hot-side at high temperatures. Reduce the heat in, and you will reduce the heat out.
Sounds like they undersized your installation in order to quote you a lower price. The efficiencies of heat pumps are well documented as are the weather patterns in your area. So, they should/could have known better.
Two solutions to this problem:
1) get a bigger/better heat pump.
2) improve you building insulation and figure out where you are losing energy.
I live in FL and we have a backup resistive heating element that kicks in as needed. Mostly only comes on a few days in the year or for short bursts when there's a cold snap that the heat pump can't keep up with.
This is fine until everyone in your neighborhood has one and it causes a brown out. (Peak amperage for the heating strips on my heat pump are three times as high as for the heat pump itself at maximum cooling load.)
[1] You can of course get a much larger heat pump to compensate, but that leaves the unit way over-sized for cooling loads.