Man on man did you open Pandora's Box.
I will try to explain the facts. Now bear in mind this is Thailand.
Technically and legally any 'falang' teacher in Thailand should have a teaching license from their respective country. Now once again bear in mind this is Thailand.
Some schools will require this while other will not. So there you go.
So why the gray area? Certainly any reputable international school will demand such documents. Ones not accrediated might not be so demanding. Thai government/private schools? It boils down on who knows who.