That's only sort of true.
Ya' see, there is a technological triangle for tread rubber involving treadwear, traction, and rolling resistance. Improve one, and you have to sacrifice one or both of the others. The best fuel economy is for tires that have both poor traction and poor treadwear. This combination is usually found in OE (Original Equipment) tires - the ones that come on new vehicles from the assembly plant. Unfortunately, they are usually "upgraded" after the OEM stops specifying them.
Tire manufacturers are keenly aware that some people want good fuel economy out of their tires, so they usually produce a line of tires labeled LRR (Low Rolling Resistance) or something similar.