The thing I dislike about the maroons most is the inconsistencies with the uniforms and collars .AFAIK, Saavik was intended to to be the acting science officer on the Grissom. The white collar indicated that she had graduated from the Academy and was in the command division, not that she was the ship's first officer. Had we even seen a Lieutenant serving as first since Number One in "The Cage"?
I believe that at the time of shooting on TWOK, Chekov was only intended to be the science officer (or perhaps the security officer) on the Reliant. His being the first officer was only something that was added to the Reliant's initial log entry after the fact. That log entry is the only time in the movie that Chekov is stated to be the Reliant's first officer.