The claim "Sulu was not under the control of the entity" is automatically false, because everybody was. Beyond that, everything about the way the heroes act is fully open to speculation. And as I outlined, Sulu being coerced to tell a lie had beneficial results for the beast - or do you forget what the direct result was?
When Chekov goes after the Klingons, against Kirk's direct direct orders, Kirk just sits back. But then Sulu claims Chekov has no brother - and it is at that point that Kirk sends not just Sulu but a Security team to do battle with the Klingons in order to recover the Ensign. A clear victory for (*).
First of all, there's no evidence that every single person was under the influence of the alien. Clearly not everyone was, because if they were, they wouldn't have figured out that they were being manipulated and figure out a way to put a stop to it. And clearly Sulu wasn't either.
And of course Kirk sends a security team to rescue Chekov: The guy's completely delusional and unpredictable, but perhaps the only evidence that something's going on that's not quite right. That's not a "clear victory" for the alien: it ultimately shows Kirk what's really going on.
Second, there are numerous times where Chekov was around Klingons in a volatile situation (The Trouble with Tribbles, STVI, etc.) and not once does he ever mention a brother that was killed by them, or acts like he absolutely hates Klingons, which is clearly at odds with his behavior in "Day of the Dove."
Verdict? Chekov was being manipulated, and Pyotr does not exist. If you want to think he does, fine, but you're picking at straws to justify your opinion.
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