No, it's more that using lower thrust during take off saves on engine wear and noise levels around the airport. It doesn't really have that big an impact on fuel use, at least that's not the primary purpose.
The article concentrates far too much on the thrust setting. The important bit is the speed where the plane should be rotated to take off, which is known as V_r. That depends on the weight of the plane. On the takeoff roll, the pilots watch the airspeed indicators and pull back to lift off when that speed has been reached. If they have been told a V_r that is lower than it should be, then pulling back will rotate the aircraft without it taking off, and that's when you have this danger of the tail hitting the ground. When that happens, the plane must be inspected, because a tail strike has the potential to weaken the pressurised container that is the fuselage, and this could lead to an explosive burst and depressurisation when flying at high altitude. See https://en.wikipedia.org/wiki/China_Airlines_Flight_611 for why this is a Bad Thing.