There are a number of different types of contracts KETs may have. Tenured teachers at PSs do need a degree in English education. Full-time contract teachers do, too. Part-time teachers / teaching-assistants don't necessarily. Then, recently there's emerged a new position of "conversation teacher", which requires a degree in any subject and a series of interviews. Depending on the province, these may not be very difficult to pass. Here's a little piece I wrote about one generic applicant: http://www.expatkorea.com/bbs/showthread.php?t=18078
Compelling writing. Is this process something you've witnessed first hand (maybe as the 'white guy')? Quite interesting for sure.