They use either LiFePO4 cells (which can be charged at up to 4C - resulting in 15 minute charge), by the way those cells exist in 18650 format too - e.g. A123Systems APR18650M1A, or they use LiMn cells, which can be charged at up to 2C - resulting in 30 minute charge, but they have higher capacity than LiFePO4.
100x higher current = 30C (as current Li-Ion’s have recommended rate of 0.3C)
30C for 500mAh cell (typical in mp3 players) = 15A
15A at 4V = 60W, quite possible solution.
Average outlets have no problems handling even 10A… but imagine how huge power brick would have to be in order to supply 420W to a laptop. Hell, even Dell’s 200W brick for Alienware laptops is monstrous, and it’s not even half of that