Yes - over the last decade or so they removed the heating element in most US dishwashers. So they either are connected to the hot water line, or have a mechanism to heat the water (or both).

I could be wrong but I'm pretty sure that even today almost all US dishwashers have some mechanism to heat the water, just maybe not the giant exposed element in the bottom like older ones. Water out of the tap is going to be on the low end of usable dish-washing temps at the very beginning of a cycle, let alone 45+ minutes later.

The reason cold or luke-warm water is a problem is that the programs are extremely simple and just assume the input is 110-120f and won't stall the cycle for waiting for the target temp.

My dishwasher doesn't have a big exposed heating element in the pan but it still has a water heater to it. It still gets the water very hot even if I start it without getting the hot water flowing first.