The e-ink panel apparently requires +15V and -15V to drive it (a total swing of 30V).
They had a goal of 21 hours of battery life. Actually due to the rate at which lithium secondary batteries decay they need to do better than that to meet the runtime spec for the warranty period of the device. A lithium secondary battery left on charger most of the time at 25C will decay 20% in one year, at 40C is will decay 35%.
To drive that big swing efficiently you want the highest battery voltage you can get away with. Since the photos reveal two 3.7V batteries my guess is that iRex is running them in series to produce a nominal 7.4V head into their switching power supply circuit.
The other technical challenge is the battery itself. Lithium batteries require a constant current charge (usually .7C where C is the mAH rating of the battery) until they reach 4.2V per cell. At this point the battery is roughly 70% charged. You then switch to constant voltage mode and let the current drop until you reach 10% of the initial constant charge current. At that point a sane charger stops.
So what does all this mean?
To charge two cells to the switch over voltage you would need a charger capable of pumping .7C into 8.4V. Rumor has it the batteries in the iLiad as 1100mAH so that's .77A at 8.4V or 6.468W of energy (ignoring losses in the charger circuit itself, and any juice the iLiad itself is using to operate.)
Supporting evidence: charger voltage specification given by jan in the iRex forum was 9V to 15V with max current draw of 1A. Covers the battery specs I propose above.
What can USB supply? Normally a USB port will supply up to 500ma at 5V. Thus USB can supply 2.5W of energy: not enough to charge the iLiad battery pack.
Motorola and others have a super-USB spec where they can source up to 1.5A at 5V. This would supply 7.5W of energy which would seem sufficient to charge the iLiad's battery. But to achieve the needed voltage the iLiad would need to boost the 5V to over the needed 8.4V in order to use it to charge the battery. This boost switching supply would be doing good to achieve 80% efficiency... .8 * 7.5W = 6W not enough juice.
Also keep in mind, that's using an external super charger, not a computer's USB port , or a regular car charger or regular cell phone wall brick charger e.g. you might as well use the iLiad charger.