Kirk recognized T'Pau. It was clear that she was the one running the ceremony.
Kirk made that assumption before any running had taken place, simply because he knew T'Pau was a leader by profession. But Elizabeth II did not run the wedding of her son, nor did Prime Minister Cameron, despite their prominent presence.
Since Kirk and McCoy had never attended a Vulcan wedding before, why wouldn't they consider everything normal?
Hmh? That's the point - they'd believe everything and have no way of knowing the truth about anything.
he was there as the original intended Champion (from his pov)
...But he might have been the only one to hold that conviction. The original claim that it was "obvious" that Stonn was to fight is the one I find dubious. The spirit of the episode would rather suggest that T'Pring had been refining her plan for years in advance, and would never have risked her beloved when logic gave her a perfect out.
Timo Saloniemi