It actually could be either. Some dishwashers have their own heater that heats the water to proper temperature, some don’t. If you have electric water heater and you are sure the instructions say use cold water, you can probably use cold. However,until this year, if you have a gas water heater, it is cheaper to use the gas to heat the water. If however, the dishwasher does not have its own heater, you are going to be washing dishes with cold water, unless you hook it to hot.
Either way, you cannot go wrong hooking up to the hot water piping. If the DW has its own heater, it will not have to heat the water as long, if it already comes in hot.
And I cannot imagine any manufacturer designing any component that would be damaged by hot water. It is a dishwasher, intended to be operated with hot water, followed by hot air circulated for drying. Heat transfer by thermal conductivity, radiation, and convection from normal dishwasher operation would certainly raise the temperature of any wetted component to at least that of the water from the hot water heater.
If the manufacturer specified cold water then they could have installed a plastic component that was not suitable for hot water. And since the fill system is external to the dishwasher tub itself, the components would not be subjected to the higher temperatures. As I originally stated, using hot water is the most common connection, but the caveat would be why the mfgr. specified cold water.