True, Kirk damns himself later, but he generally tended to blame himself when he lost crewmen. Should he have been more prudent? In this case, yes. But Kirk didn't get to where he was by being overly cautious. He's a by-the-book kind of guy, but also a he's also humanist/altruist who is willing to take risks. We don't know that he broke any rules here, but we do get the sense our hero's intuitive guesses can't all be right.
But he has absolutely no reason to not be cautious here. False orders in his name, jammed communications then Regula One going silent plus the ship attached to the project refusing to respond to hails. That is about 2+2=4 as it gets.
Kirk has to act very unKirk like in order for the story to move forward.