There are a few flaws with the source. But first, let me start off with a disclaimer that by "complete discharge" I do not mean "0% remaining" - I mean when the phone shuts itself off due to low power. Completely discharging a battery past the threshold that phones and laptops set (about 3%) is much more damaging than partial discharge charging could ever be.
Anyway, let me continue here. First thing I noticed was the fact that they showed graphs for lithium polymer batteries for Figure 1. Lithium polymer and lithium ion batteries are very different technologies and work very differently.
If you look at Table 2, you will see that a 10% discharge will result in 4700 charge cycles while a 100% discharge will result in 500 cycles. If you do the math, the 10% discharge gives you 470 full cycles worth of battery charge. That does not seem very attractive. However, the 50% result giving 1500 cycles is interesting - that's 750 full cycles worth. Perhaps there is some merit there, and some discharge level that is best for the battery.
Anyway, from my understanding, the whole full discharge thing was a much bigger problem with nickel-metal hydride batteries. It had to do with sending a current through the battery while the chemical reaction had not completely proceeded in the operational direction, forcing the reaction to reverse early, resulting in some wear and tear. Lithium ion batteries are built differently and the backing technology is always improving, so the "memory effect" is probably not as prevalent anymore.
If you observe people with laptops, though, the ones that complain the most about their battery life being extremely short are those that plug in their laptops whenever they get the chance and use the battery when they don't. That should be saying something.