There's a difference between being driven loud and driven well ... an iPhone will drive 600ohm DT880s pretty loudly, but they sound rubbish compared to when properly amped. The K601 / K612 needs an amp to perform at it it's absolute best.
However, it doesn't need a lot of amping - I ran mine perfectly well off a FiiO E10 and in fact I couldn't tell the difference between that and with my M-stage. Both sounded better than directly out of my iPhone. The difference isn't huge, but it is there, especially for demanding music (e.g. stuff with a wide dynamic range).