In the court room, didn't Shaw specifically request a close up of the small control panel on the captains chair?.
I don't think the computer did it on it's own accord.
.
You're right- I had forgotten that:
================
SHAW: Reverse. Stop. Go forward with magnification on the panel. Freeze that. Captain Kirk is now signalling a Yellow Alert. Go forward, normal view.
[Bridge]
(On courtroom viewscreen.)
UHURA: Call from the pod, sir.
KIRK: Tie in.
FINNEY [OC]: Finney here, Captain. Ion readings in progress.
KIRK: Make it fast, Ben. I may have to go to Red Alert.
FINNEY [OC]: Affirmative.
KIRK: Hold our course, Mister Hanson.
HANSON: Aye, aye, sir. Natural vibrations, force two, Captain. Force three.
KIRK: Engineering, then ion pod.
UHURA: Aye, aye, sir.
CREWMAN [OC]: Engineering.
KIRK: One third more thrust.
CREWMAN [OC]: Working.
FINNEY [OC]: Ion pod.
KIRK: Stand by to get out of there, Ben.
FINNEY [OC]: Aye, aye, sir.
HANSON: Force five, sir.
KIRK: Steady as she goes, Mister Hanson.
(And the close up on the Captain's panel shows...)
[Courtroom]
SHAW: Freeze that! If the court will notice, the log plainly shows the defendant's finger pressing the jettison button. The condition signal reads Yellow Alert. Not red alert, but simply Yellow Alert. When the pod containing Lieutenant Commander Finney was jettisoned, the emergency did not as yet exist.