Wait, are you implying that two different sources outputting the same voltage to the same headphones (thus same volume) will provide different total amounts of current? I think I understand what you're trying to say, but please take another look at Ohm's Law or something similar.
Anyway, to answer the original question, this means that the internal amplifier in the iPod is capable of enough voltage to make it loud enough for you with the music you listen to, probably without clipping. A different amplifier or source may just be able to drive the K701 more accurately, as in the output voltage waveform to the headphones may be closer to what's actually in the music file. Lower-quality amplifiers and the DACs (digital-to-analog converters) behind them will distort the output (more) in various ways, given different loads and conditions.
Whether or not pursuing more expensive equipment to get a somewhat cleaner signal to the K701 is worth the additional cost and bulk/weight carrying around, is up to you. Keep in mind that the headphones themselves distort some too, and they have significant frequency response variations and other oddities.