Beyond the citation though, it makes logical sense. The mechanism for sanitation is that the soap itself destroys the bacteria. This mechanism works regardless of temperature. Cold water + Soap should be just fine as long as your hands are otherwise visibly clean.

In the food industry, we were required to use high temperature water. This was presumably to remove actual surface contaminants (dirt, grease, other food contaminants) rather than for actual sanitation. That's why you might still see guidelines for using hotter water temperatures.