it's been a while since I watched TWOK but I don't think they ever referred to it as "the Klingon Neutral Zone", just "the Neutral Zone" ( or "the Zone".)
You're right. I had misremembered that. Still, the presence of the Klingon ships still confuses the issue. In context, it's hard to read it as anything other than the Klingon
Neutral Zone. Although the Klingons catch the Enterprise off guard, there's no indication from anyone that their appearance is a surprise.
I suppose, like you argue, it could be a fiction that doesn't represent the "reality" (heh) of the rest of the Star Trek universe, but wouldn't that undermine the point of the test?