Was Jamie In On It?

She was also a trusted friend and possibly a former lover.

 

I think somehow Jamie figured out what her father had done. She didn't want any further investigation that might reveal the truth. She also had no reason to want Kirk dishonorably discharged. She didn't want him forced to take a desk job either, but her main goal was to stop any further investigation.

Cogley appears to be figuring it out, unless he just makes laconic comments to his clients to make it seem like he's on the verge of a breakthrough: "No, but I may be getting ready." I suspect that someone involved in the show changed it, wanting the shows stars to solve the problem, rather than have a guest star solve it. They later went that route in Assignment Earth, but for a possible spinoff. They didn't want to do it in Court Martial.

They had to have Spock find the computer tampering. Then Cogley could act on his suspicion that Finney was still alive. I don't see a good reason not to bring this up before the computer tampering was discovered. In any case, to me the show implies that Cogley came up with his claim Finney was alive based on the computer tampering plus his earlier suspicion about Jamie.