I can understand the apparent conflict, but there is an explanation and the Boeing author is correct.
Often, an operator pays a consultant or manager to develop or handle a fuel conseravtion program, and so the operator wants to see immediate results. The easiest way to do this using cost index, and in fact a good starting point, is to develop a general philosophy within the business organization as to how much fuel (cost) is worth how much time (cost). This is a generalization, a basic number, quickly accomplished in consulation with the accounting folks, flight ops folks, and even customer service folks. The typical result is often seen on the line when you get a bulletin that says "effective immediately enter a cost index of XX for the XYZ fleet." Use of that value will generally result in a very measuarable and meaningful fuel and dollar savings.
But to take full advantage of the potential inherent in the use of Variable Cost Index, the operator has to take into account the individual circumstances or drivers that affect a particular flight, and which may alter the original assumptions used to determine a tollerance for time related costs. Some of these circumstances might be:
...Noise curfew, passenger misconnects, temperature performance penalties, crew legalities, potential for loss of slots, gate availability, aircraft routings, maintenace plans, etc.. These situtations carry costs not considered in the formula for calculating aircraft related time costs. Often, these issues are not readily apparent to the flightcrew, and require oversight / coordination within SOC and custormer service. There is a need to quantify the associated potential costs when a flight fails to arrive within a certain period of time from that originally scheduled. If management has that data and can apply that to the situation at hand, an analysis can be made in which a higher cost index can be considered, and selected if appropriate. Again it's worth pointing out that there is definitely a limit to what can be done......you can literally push tons of fuel out the tailpipe for one or two minutes reduction in time costs....normally a poor investment. If the analysis shows that the time savings are adequate to avoid the undersired consequences of late arrival and the associated costs outside the normal calculation of cost index, then the decision to use the higher value is based on the financial result.
Because this takes people to calculate and manage....most airlines do not take full advantage of this capability.