It's the degree they want.
I have my CELTA, from Bournemouth, England. Unfortunately it means nothing to most schools over here. It's the degree they want to see. 'You have no TEFL or CELTA, but no problem because you have a degree' - you can teach.
Thai schools are full of foreign teachers who have no TEFL qualification whatsoever, but do have a 'degree' which in many cases was obtained through dubious channels. Just go into a class and start writing stuff on the white board, and hope no one takes too much notice.
Last week. one of these guys at my school marked down several classes for using the verb to dote. He had never heard of it. 'My mother dotes on me' He asked me why do the students keep writing 'dots on, dots on' ?
It seems to me that you need a particular kind of arrogance to walk into a classroom without the proper qualification under your belt.