Reposting this (but again, I can’t vouch for it):
Yes, some schools seem willing to accept only people from the seven countries.
Back in 2012, I had a co-worker who was from Singapore. As far as I know, he was hired as a foreign English teacher. I don’t think he was paid as much as a typical foreign English teacher, and I also think he was hired under special circumstances. Additionally, I think he had a U. S. Bachelor’s degree. I don’t recall seeing his work permit. However, one day we got inspected (I don’t know whether it was local or national), and afterward, if I recall correctly, he confirmed to me that his work permit was for a foreign teacher. He even remarked that the inspector was surprised and that she said that it was the first one of its kind that she had ever seen.
I think this was around the time that Forumosa was having a dispute about whether one had to be from one of the seven countries. I didn’t mention my co-worker during that dispute, because I didn’t want to drag him into it. However, as far as I can tell (from Facebook), he passed away in 2018, so I guess it’s okay to mention him now.