Some people never knew what happened during Age of Discovery, what havoc the invasions had wreck on the Asian countries. There were inter-marriage between east and west more than a thousand years ago. It is rare but not unlikely.
I agree with you it is somewhat possible. Consider this; a thousand years ago, we Hungarians (Magyars) looked like my avatar, (bigger picture; http://arpad.org/wp-content/uploads/2012/02/Arpad_Kertai-Zalan600.jpg). We had very Mongol-like faces, though bonier and with more almond-shaped eyes and high cheekbones. Then we settled in Europe, and now most Hungarians look more like Eastern Europeans than people of the Russian/Mongol steppes, however there are exceptions (many exceptions) such as me, who still posses almond eyes and high cheekbones. Thus, I think that blue-eyed Koreans are plausible though much less so (remember it was only a few explorers in the midst of vast populations, and I hardly think their top priority was...well breeding). However, I'm not saying that this makes the OP's post any more or less believable.